Fractions, Decimals, and Probability

Question 1

What is a fraction?

Answer 1

A fraction is a part of a whole.

Example: ³/₄

Question 2

What is a numerator?

Answer 2

The top number of a fraction is called the numerator.

The numerator shows how many equal parts of a whole are in the fraction.

Question 3

What is a denominator?

Answer 3

The bottom number of a fraction is called the denominator.

The denominator indicates how many parts make up a whole.

The denominator cannot equal zero.

Question 4

What is a simple fraction?

Answer 4

In simple (common) fractions, both the numerator and the denominator are integers expressed as a ratio.

Examples: ³/₄, ¹/₃

These are the types of fractions you’ll see most often on the SAT.

Question 5

What is a simplified fraction?

Answer 5

In simplified fractions, the greatest common factor of both the numerator and the denominator is 1.

Examples: ¹/₂, ³/₄

Question 6

What fractions are called proper fractions?

Answer 6

In proper fractions, the numerator is less than the denominator.

Examples: ¹/₄, ³/₄

Question 7

What fractions are called improper fractions?

Answer 7

In improper fractions, the numerator is equal to or greater than the denominator.

Examples: ²³/₁₁, ⁹/₇

Question 8

What fractions are called equivalent fractions?

Answer 8

Equivalent fractions have the same value, but are expressed differently.

Examples: ¹/₂, ²/₄, ³/₆

Question 9

What are similar fractions?

Answer 9

Similar fractions have the same denominator.

Examples: ¹/₄, ³/₄

Question 10

When the numerator of a fraction is zero, the fraction is….?

When the denominator of a fraction is zero, the fraction is…?

Answer 10

When the numerator of a fraction is zero, it’s called a zero fraction. It equals 0.

When the denominator of a fraction is zero, the fraction is undefined.

Remember, nothing can be divided by 0.

Question 11

What are reciprocal fractions?

Answer 11

In reciprocal fractions, the numerators and the denominators are switched.

Examples: 5 is a reciprocal of ¹/₅.
³/₈ is a reciprocal of ⁸/₃.

Question 12

What are complex fractions?

Answer 12

In complex fractions, the numerator and the denominator are fractions themselves.

Example:

Question 13

What are mixed fractions?

Answer 13

Mixed fractions combine an integer and a proper fraction.

Example: 6 ²/₃

Mixed fractions are also called mixed numerals or mixed numbers.

Question 14

How do you simplify a fraction by using the GCF (greatest common factor)?

Answer 14

Divide both the numerator and the denominator by their GCF.

Example: Simplify ²⁴/₃₆

The GCF of 24 and 36 is 12. Simplify the fraction by dividing by 12. The lowest term of this fraction is ²/₃.

Question 15

How do you use prime factorization to simplify a fraction?

Answer 15

Write out the prime factorization of both the numerator and the denominator and cancel out any common prime factors.

Example: Simplify ⁷⁶/₈₄

Question 16

How do you reduce a fraction to its lowest terms?

Answer 16

To reduce a fraction to the lowest terms, factor out both the numerator and the denominator. Then, cancel out all common factors.

Example: ¹⁶/₂₄ = ^{4 x 2 x 2}/_{4 x 2 x 3} = ²/₃

Question 17

How do you add or subtract fractions that have the same denominator?

Answer 17

When fractions are similar (i.e. have like denominators), work with the numerators (add or subtract) and leave the denominators alone.

Example: ⁵/₂₂ + ⁷/₂₂ = ¹³/₂₂

Question 18

What is the Least Common Denominator (LCD) of two or more fractions?

Answer 18

The Least Common Denominator (LCD) of two or more fractions is the smallest whole number that is divisible by each of the denominators.

Question 19

How do you find the LCD of two or more fractions?

Answer 19

To find the LCD, use the same methods used to find the Least Common Multiple (LCM) of two numbers:

Successive multiplication Prime factorization See “Factors and Multiples” deck for detailed explanation.

Question 20

How do you add or subtract fractions with different denominators?

Answer 20

To add or subtract fractions with different denominators:

Find the LCD

Write equivalent fractions with the LCD

Add or subtract the numerators

Example: ¹/₅ + ²/₇ = ⁷/₃₅ + ¹⁰/₃₅ = ¹⁷/₃₅

Question 21

How do you multiply fractions?

Answer 21

• To multiply fractions, simply multiply the numerators, then multiply the denominators.
• It doesn’t matter whether fractions have same or different denominators.
• Use cancelling whenever possible as a shortcut. Cancelling can take place only between numerators and denominators.

Question 22

How do you divide fractions?

Answer 22

Rewrite the second fraction as its reciprocal and multiply by the first fraction.

Example: ⁵/₆ ÷ ²/₃ = ⁵/₆ x ³/₂ = ¹⁵/₁₂ = ⁵/₄

Question 23

How do you turn an improper fraction into a mixed number?

Answer 23

To convert an improper fraction into a mixed number, divide the numerator of the improper fraction by its denominator. If there is a remainder, it will become the numerator of the mixed number.

Example: ¹⁸/₁₄ = 1 ⁴/₁₄ = 1 ²/₇

Question 24

How do you turn a mixed number into an improper fraction?

Answer 24

To convert a mixed number into an improper fraction, multiply the denominator by the whole number and add the numerator. This number becomes the numerator of your improper fraction.

Example: 1 ²/₃ = ⁵/₃
3 * 1 + 2 = 5 It’s the numerator of the improper fraction.

Question 25

How do you add or subtract mixed numbers containing similar fraction parts?

Answer 25

Add or subtract the fraction parts first, then work with the whole numbers. Simplify if possible.

Examples: 5³/₇ + 8²/₇ = 13⁵/₇
5³/₇ + 8⁶/₇ = 13⁹/₇ = 14²/₇

If the answer contains an improper fraction, you must turn it into a mixed number.

Question 26

How do you subtract mixed numbers with similar fraction parts when the numerator of the second number is greater than the numerator of the first number?

8³/₇ - 5⁶/₇= ?

Answer 26

“Regroup,” or remove 1 (or ⁷/₇) from the whole part of the first mixed number by adding it to the fraction part:

8³/₇ - 5 ⁶/₇= 7¹⁰/₇ - 5⁶/₇

Perform the subtraction, dealing first with the fractions, then the whole numbers:

7¹⁰/₇ - 5⁶/₇ = 2⁴/₇

Question 27

How do you add or subtract mixed numbers with different denominators?

5³/₅ + 8¹/₄ = ?

Answer 27

5³/₅ + 8¹/₄ = ?

Write equivalent fractions using the LCD of 4 and 5.

5³/₅ = 5¹²/₂₀ ; 8¹/₄ = 8⁵/₂₀

Add the fraction parts, then the whole numbers:

5³/₅ + 8¹/₄ = 5¹²/₂₀ + 8⁵/₂₀ = 13¹⁷/₂₀

Question 28

How do you subtract mixed numbers with different denominators?

8³/₇ - 5²/₃ = ?

Answer 28

Using the LCD of 3 and 7, write new equivalent fractions :

8³/₇ - 5²/₃ = 8⁹/₂₁ - 5¹⁴/₂₁

Make a new fraction equal to 1 and “regroup,” or remove, that fraction from the whole part of the first mixed number by adding it to the fraction part:

8⁹/₂₁ = 7³⁰/₂₁

The fraction in the first mixed number is now greater than the fraction in the second number. Subtract the fractions first, then the whole numbers:

7³⁰/₂₁- 5¹⁴/₂₁ = 2¹⁶/₂₁

Question 29

How do you multiply or divide mixed numbers?

Answer 29

Change mixed numbers into improper fractions and follow the rules explained in “Multiplying and Dividing Fractions” cards.

Question 30

What is decimal notation?

Answer 30

Decimal notation is the most common way to write the base 10 numeral system, which uses digits from 0 to 9 together with the decimal point (.)

Question 31

What is a decimal fraction?

Answer 31

A decimal or decimal fraction is a fraction whose denominator is 10 or a power of 10.

Adding zeros to the right side of a decimal fraction does not change its value.

Examples: 0.62; 0.5; 0.009

The above numbers can be written as proper fractions:
⁶²/₁₀₀; ⁵/₁₀; ⁹/₁₀₀₀

Question 32

What is a mixed decimal?

Answer 32

A mixed decimal is a number consisting of an integer plus a decimal fraction.

Examples: 5.34; 654.006; 1.1

Question 33

What decimals are called similar decimals?

Answer 33

Similar decimals are decimals that use the same number of places to the right of the decimal point.

Examples: 7.345 and 2.012

Question 34

What is a periodic decimal?

Answer 34

A periodic (or repeating) decimal is a non-terminating decimal with repeating digits or group of digits.

Example: ¹/₃ = 0.33333333…….

One way to indicate a repeating decimal is to put a horizontal line above the repeated numerals.

Question 35

What is a non-repeating, non-terminating decimal?

Answer 35

A decimal that neither terminates nor repeats is called a non-repeating, non-terminating decimal.

Example: 1.41421356237……..

Question 36

How do you convert a fraction into a decimal?

Answer 36

Just divide the numerator by the denominator (if the denominator doesn’t equal 10, 100, 1000, etc)

Example: ⁵/₈ = 0.625

Question 37

Besides dividing the numerator by the denominator, what is another way to convert fractions into decimals?

Answer 37

Multiply both the numerator and the denominator by such number that makes the denominator 10, 100, 1000, etc.

Question 38

How do you convert a decimal number into a fraction?

Answer 38

The key is to understand the place value of the decimal.

Read the decimal: the 1st place to the right of the decimal point indicates tenths, 2nd place indicates hundredths, 3rd place indicates thousandths.

Example: 0.145 = ¹⁴⁵/₁₀₀₀ = ²⁹/₂₀₀

Question 39

How do you mutiply a decimal number by a power of 10?

Answer 39

To multiply a decimal by a power of 10, move the decimal point to the right, one place for each zero in the power of 10.

Example: 15.8567 x 100 = 1585.67

Question 40

How do you divide a decimal number by a power of 10?

Answer 40

To divide a decimal number by a power of 10, move the decimal point to the left, one place for each zero in the power of 10.

Example: 15.86 ÷ 1000 = 0.01586

Question 41

How do you add or subtract decimals with different number of decimal places?

Answer 41

To add or subtract decimal numbers, align them first.

Tenths have to be under tenths, hundredths - under hundredths, etc. The decimal point in the answer goes right under the decimal points of the numbers you are calculating.

If one number has more decimal places than the other, add zeros to the right end.

Question 42

When you multiply decimal numbers, what is the number of decimal places in the product?

Answer 42

The number of decimal places in the product is the sum of the decimal places in the numbers you are multiplying.

Example: 2.3 x 1.1 = 2.53

Multiply the numbers as if they were whole numbers. Each factor has one decimal place so the answer would have two decimal places.

Question 43

How do you divide by a decimal number?

Answer 43

In order to divide by a decimal:

• Convert the divisor to a whole number by multiplying by a power of 10
• Multiply the dividend by the same power of 10

Example: 34 ÷ 0.17 = 3400 ÷ 17 = 200

Turn 0.17 into a whole number by multiplying by 100. Then, multiply 34 by 100 as well.

Question 44

Define:

probability

Answer 44

Probability is the likelihood or a chance that a random event will occur.

The probability that one event will or will not happen is a simple probability.

The probability that two or more events happen is a compound probability.

It’s denoted as P (A) - probability of an event A.

Question 45

How do you express probability as a number?

Answer 45

Probability can be expressed as a number between 0 and 1.

“0” probability means that the event is impossible. “1” probability means that the event will certainly take place.

Probability can also be expressed as a percentage between 0% and 100%.

Question 46

How do you calculate the probability that an event will take place?

Answer 46

The probability of an event happenning is the number of favorable outcomes over the total number of possible outcomes.

Example:
Out of 24 tops in your closet, 8 have long sleeves and the rest have short sleeves. What is the probability that at random you pick a short sleeve top?

16 short sleeve tops over 24 total tops

¹⁶/₂₄ = ²/₃

Question 47

What is the probability that an event A will not happen?

Answer 47

The opposite of an event A is the event not A. Its probability can be expressed as:

1 - P (A).

Example:
What is the probability of not rolling two on a six-sided die?
1 - (chance of rolling two) = 1 - ¹/₆ = ⁵/₆

Question 48

Define:

independent events

Answer 48

Two events are independent when the outcome of the 1st event doesn’t affect the outcome of the 2nd event.

Example:
Two decks of cards…. pulling a king from each one.

P₁(K) = ⁴/₅₂ = ¹/₁₃
P₂(K) = ⁴/₅₂ = ¹/₁₃

Question 49

Define:

dependent events

Answer 49

Two events are dependent when the outcome of the 1st event affects the outcome of the 2nd event.

Example:
Pulling a king from a deck of cards, then, without replacement, pulling a queen.

P (K) = ⁴/₅₂ = ¹/₁₃
P (Q) = ⁴/₅₁

Question 50

If two events A and B are independent, what is the probability of both of them happening?

Answer 50

The probability of two independent events A and B happening is a product of a probability of event A and a probability of event B.

P (A and B) = P (A) x P (B)

Example:
What is a probability of having two tails when you flip two coins?
¹/₂ x ¹/₂ = ¹/₄

Question 51

When two events A and B are dependent, what is the probability of both of them happening?

Answer 51

The probability of two dependent events A and B happening is a product of a probability of A and a probability of B after A occurs.

P (A and B) = P (A) x P (B given A)

Example:
A drawer contains 3 white tee-shirts and 4 black tee-shirts. Find a probability of first pulling a white tee-shirt and then, without replacing, pulling a black tee-shirt.

³/₇ x ⁴/₆ = ²/₇

The total number of possible outcomes of the 2nd event is smaller than the number of possible outcomes of the 1st event.

Question 52

Define:

mutually exclusive events

Answer 52

Mutually exclusive events are events that cannot occur at the same time.

Example: Probability of rolling 2 or 4 on a six-sided die….

Question 53

If two events A and B are mutually exclusive, what is the probability of either of them occuring?

Answer 53

The probability of either of mutually exclusive events A or B happening is a sum of the probability of event A and the probability of event B.

P (A or B) = P (A) + P (B)

Example:
What is a probability of rolling 2 or 4 on a six-sided die?

¹/₆ + ¹/₆ = ¹/₃

Question 54

What do the words “without replacement” mean in the context of a probability problem?

Answer 54

The words “without replacement” mean the number of possible outcomes of an event following the 1st event is reduced.

Example:
There are 6 apples in a fruit bowl; 4 green and 2 red. What is the probability of picking a red apple after you have picked a green apple from the bowl, without replacement?

There are 2 red apples out of 5 apples left in the bowl so, it’s ²/₅. Had you put the green apple back in the bowl, the probability of picking a red apple would have been 2 out of 6.

Question 55

How do you know when to multiply probabilities of different events or when to add them?

What words can give you the clues?

Answer 55

When you see the words “both”, “all”, “together”, “combined”, multiply the probabilities of different events.

When you see “either…. or”, add them.

Example:
What is the probability of picking BOTH 2 and 4 out of a set of numbers from 0 to 9 (with replacement)?
¹/₁₀ x ¹/₁₀ = ¹/₁₀₀

Example:
What is the probabiltiy of picking 2 OR 4 from the set of numbers from 0 to 9 (with replacement)?
¹/₁₀ + ¹/₁₀ = ²/₁₀

Question 56

There are 6 apples in a fruit bowl; 4 green and 2 red. What is the probability that a green apple is picked and then a red apple is picked, assuming no replacement between turns?

Certain words in this problem give you clues how to solve it. What are they?

Answer 56

The “clues” words are no replacement.

⁴/₆ is the probability of picking a green apple. Since you didn’t replace the apple, the probability of picking a red apple after you had pick the green apple is ²/₅. The number of possible outcomes in the probability number of the 2nd event is reduced by 1.

Since you are looking for the probability of both events happening, multiply probabilities of each event.

⁴/₆ x ²/₅ = ⁴/₁₅

Question 57

What is the essense of the Fundamental Counting Principle?

How do you count the total number of possibilities for several events to occur?

Answer 57

The Fundamental Counting Principle: If there are “a” ways for one activity to occur, and “b” ways for a second activity to occur, there are a x b ways for both to occur.

Simply multiply the number of ways each activity can occur to count the total number of possibilities.

Example:
There are 6 pairs of jeans and 8 tops in your closet. How many outfits can you build out of those?
6 x 8 = 48

Question 58

What are the two ways you can simplify a fraction?

Simplify ³⁶/₉₀ using both methods.

Answer 58

• Divide by GCF

The GCF of 36 and 90 is 18. Divide both number by 18 to reduce the fraction to its lowest term ²/₅.

• Cancel out common prime factors

Factor both 36 and 90 into primes and cancel out common factors.

Question 59

What is the reciprocal fraction of ¹³/₂₅?

What type of fraction is the answer?

Answer 59

The reciprocal of ¹³/₂₅ is ²⁵/₁₃.

It’s an improper fraction.

Remember, you need to convert it into a mixed number.
²⁵/₁₃ = 1 ¹²/₁₃

Question 60

A prime number multiplied by its reciprocal will always be:

(a) even
(b) odd
(c) prime
(d) 0

Answer 60

(b) odd

Note: The product of any number and its reciprocal equals 1.

Question 61

If you divide a prime number by its reciprocal, the result will never be:

(a) even
(b) odd
(c) prime
(d) 4

Answer 61

(c) prime

Dividing a number by its reciprocal is equivalent to multiplying the number by itself. Therefore, the result can never be prime.

Question 62

What is the reciprocal of

(1 + ⁶/₇):

(a) 1 + ⁷/₆
(b) ¹³/₇
(c) ⁶/₁₃
(d) ⁷/₁₃

Answer 62

(d) ⁷/₁₃

The expression in the parenthesis equals ¹³/₇. The reciprocal of this fraction is ⁷/₁₃.

Question 63

What is the reciprocal of the quotient of

(5 ÷ ¹/₂₅)?

(a) 125
(b) ¹/₅
(c) 5
(d) ¹/₁₂₅

Answer 63

(d) ¹/₁₂₅

Take the reciprocal of ¹/₂₅ and multiply by 5 to find the quotient. The quotient is 125. Then, flip that number to find the reciprocal.

Question 64

What operation in arithmetic requires finding the LCD?

Answer 64

Adding or subtracting fractions with the different denominators requires you to find the Least Common Denominator.

Question 65

Of the following, which is the closest to 0.6?

(a) ⁴/₅
(b) ¹⁹/₃₀
(c) ⁸/₁₅
(d) ¹¹/₁₈

Answer 65

(d) ¹¹/₁₈

The LCD of these 4 fractions is 90. Write equivalent fractions with 90 in the denominator and compare.

(a) ⁷²/₉₀
(b) ⁵⁷/₉₀
(c) ⁴⁸/₉₀
(d) ⁵⁵/₉₀

0.6 equals ⁵⁴/₉₀. Evaluate ⁵⁷/₉₀ and ⁵⁵/₉₀, because the other two choices are clearly out. ⁵⁷/₉₀ is ³/₉₀ (or ¹/₃₀) removed from 0.6. ⁵⁵/₉₀ is ¹/₉₀ removed from 0.60.

Question 66

What is the value of

³/₄ x ⁷/₈ x ¹⁶/₂₁

rounded to the nearest whole number?

Answer 66

The product of the three rounded numbers is 1.

Always look for ways to simplify fractions before operating with them. Notice that you can cancel out common factors before multiplying numbers in the numerators and the denominators. So, the simplified fraction is ¹/₂. Rounded to the nearest whole number it’s 1.

Remember, cancelling takes place only between the numerator and the denominator.

Question 67

Is the quotient of a mixed number and a proper fraction greater than or less than 1?

Answer 67

The quotient is greater than 1.

Any mixed number can be expressed as an improper fraction, and is greater than 1. Dividing by a fraction means multiplying by a reciprocal of that fraction. A reciprocal of a proper fraction is an improper fraction, which is greater than 1. The product of two numbers greater than 1 is itself greater than 1.

Question 68

What type of number is the quotient

(2 ÷ 3) ÷ (4 ÷ 5) = ?

(a) mixed number
(b) odd number
(c) even number
(d) proper fraction

Answer 68

(d) proper fraction

²/₃ ÷ ⁴/₅ = ²/₃ x ⁵/₄ = ⁵/₆

Question 69

(2 ÷ 3) ÷ (4 ÷ 5) = ⁵/₆

Would it affect the result if the parentheses are removed?

2 ÷ 3 ÷ 4 ÷ 5 = ?

Answer 69

Yes, the removal of the parentheses affects the result.

According to the order of operations rule, when the operations have the same rank, work from left to right.
²/₃ ÷ 4 = ²/₃ x ¹/₄ = ¹/₆¹/₆ ÷ 5 = ¹/₆ x ¹/₅ = ¹/₃₀

Question 70

Is the product of ten proper fractions less than or greater than 1?

Answer 70

The product of ten proper fractions is always less than 1.

In a proper fraction, the numerator is always smaller than the denominator. Multiplying ten proper fractions will give you a fraction with the numerator that is smaller than the denominator.

Question 71

Which number is greater:

the product of ³/₄ and ⁸/₃

or

the sum of ³/₄ and ⁴/₃?

Answer 71

The sum is greater than the product.

³/₄ x ⁸/₃ = 2
³/₄ + ⁴/₃ = ⁹/₁₂ + ¹⁶/₁₂ = ²⁵/₁₂ = 2¹/₁₂

Find the LCD when you add fractions with the different denominators.
Remember to change improper fractions to mixed numbers and reduce fractions to lowest terms when possible.

Question 72

Total population of towns A, B and C in France is a certain whole number. The population of town B is one-third of the population of town A. The population of town C is four times the population of town B. What fraction of the total is the population of town B?

Answer 72

The population of town B is ¹/₈ of the total.

The population of town A is not related directly to the population of town C. The common element between them is town B’s population. So, express their respective populations in terms of B.

Total population (T) = A + B + C.
B = ¹/₃ A ⇒
A = 3B; C = 4B
Substitute the equivalents of A and C in the equation and solve for B.
T = 3B + B + 4B = 8B ⇒ B = ¹/₈T

Question 73

Complete the statement:

If you write a decimal number as a fraction, the denominator of that fraction is always….?

Answer 73

The denominator is a power of 10.

Question 74

What are the tens and tenths digits of ¹⁸²/₈ written in decimal form?

Answer 74

The tens digit is 2. The tenths digit is 7.

¹⁸²/₈ = 22.75

Question 75

How many decimal places does the product of numbers below have?

0.5 x 0.5 x 0.5

Answer 75

The result, 0.125, has three decimal places. The number of decimal places in a product is equal to the sum of the number of decimal places in factors.

Question 76

Convert ⁴/₁₂₅ into a decimal number.

Answer 76

0.032

Convert ⁴/₁₂₅ to a fraction with the denominator of 1000 by multiplying both the numerator and the denominator by 8.

Question 77

Which pair consists of two unequal numbers?

(a) 3.5, ⁷/₂
(b) 0.032, ⁴/₁₂₅
(c) ⁹⁰/₃₈, ⁵/₂
(d) ²⁰¹/₃, 67

Answer 77

(c) ⁹⁰/₃₈ and ⁵/₂ are not equal.

Question 78

Which of these numbers cannot represent the probability of an event?

(a) - 0.5
(b) 0.5
(c) 0
(d) 1.1
(e) 104%
(f) 20%

Answer 78

(a), (d), (e)

cannot express the probability because the probability is always greater than or equal to 0 and less than or equal to 1. In percents, the probability lies between 0% and 100%.

Question 79

If a card is drawn from a deck of cards at random, what is the probablity of getting a king?

Answer 79

⁴/₅₂ = ¹/₁₃

There are 52 cards in a deck. There are 4 kings among them. Therefore, there are 4 possible choices out of 52 total choices.

Question 80

There are 5 cans of Coke, 3 cans of Sprite, 4 bottles of spring water and 8 bottles of ice tea in a cooler. What is the probability, in percent, of getting a drink other than a soda can?

Answer 80

60%

¹²/₂₀ = ⁶/₁₀

There are 12 non-soda drinks in a cooler that contains a total of 20 cans and bottles.

Question 81

If two dice are rolled, what is the probability that the sum is equal to 5?

Answer 81

⁴/₃₆ = ¹/₉

There are 4 possible choices that give you the sum of 5. {1, 4}; {2, 3}, {4, 1} and {3, 2}.

By using the fundamental counting principle, you can find the total number of choices. Each dice has 6 sides; i.e. 6 possible choices. 6 x 6 = 36

Question 82

There are 5 white, 8 black and 4 multicolor t-shirts in your closet. In three days, you’ve worn one of each color and removed them from the closet.

What is the probability of you picking a multicolor t-shirt on the 4th day?

Answer 82

³/₁₄

4th day: There are 14 tee-shirts left in the closet. Among them there are 3 multicolor t-shirts.

Question 83

There are 5 white, 8 black and 4 multicolor t-shirts in your closet. In three days, you’ve worn one of each color and removed them from the closet.

What is the probability of picking a multicolor t-shirt on the 4th day and (without replacing the multicolor t-shirt) picking a white t-shirt on the 5th day?

Answer 83

The probability of both events happening equals a product of probabilities of two events.

³/₁₄ x ⁴/₁₃ = ⁶/₉₁

These events are dependent since the t-shirts were pulled without replacement.
4th day: The probability of picking a multicolor t-shirt is ³/₁₄.
5th day: The probability of picking a white t-shirt is ⁴/₁₃.

Question 84

How many different ways can three students occupy four seats in a classroom?

Answer 84

There are 12 different ways for 3 students to occupy 4 chairs.

Each student has four choices to select a seat. There are three students; therefore, alltogether, they have 12 possible choices of selecting a seat in a classroom.

Simply multiply the number of ways each activity can occur to count the total number of possibilities.