Counting and Probability

Question 1

What is the basic counting principle?

Answer 1

If there are n₁ ways to do one thing (outcomes of one experiment) and n₂ ways to do another thing (outcomes of another experiment), then there are n₁ * n₂ ways to do both.

Question 2

What can the basic counting principle be generalized as, in terms of k number of experiments?

Answer 2

The total number of outcomes of k experiments is: n₁ * n₂ * n₃ * ——– * nₖ

Question 3

What is the formula for arranging n number of distinct objects in n slots, -where ordering matters-?

Answer 3

(n)(n - 1)(n - 2)(n - 3) ————— (2)(1) = n!

Question 4

What is the formula for the number of ways of filling n slots with n objects, where ordering matters, if n₁ of them are of the first kind, n₂ are of the second kind, and n₃ are of the third kind?

Answer 4

n!/[(n₁!)(n₂!)(n₃!)]

Question 5

How do you calculate the number of outcomes with restrictions on the selections?

Answer 5

First fill the boxes that come with the restriction by the number of outcomes, before filling the other boxes with the number of possible outcomes.

Question 6

What are permutations without repetition?

Answer 6

The various ways in which r number of objects (a subset) may be selected from n number of distinct objects (a set) without replacement (without repetition) and where ordering matters.

Question 7

What is the formula for permutations without repetition?

Answer 7

n!/(n - r)!

Question 8

What are combinations without repetition?

Answer 8

The various ways in which r number of objects (a subset) may be selected from n number of distinct objects (a set) without replacement (without repetition) and where ordering does not matter.

Question 9

What is the formula for combinations without repetition?

Answer 9

n!/r!(n - r)!

Question 10

What is probability?

Answer 10

Probability is a number estimating the likeliness of an event happening.

Question 11

Does probability tell us exactly what will happen?

Answer 11

No, it is just a guide for what may happen.

Question 12

What is the formula for the probability of an event happening?

Answer 12

favorable outcomes / total number of possible outcomes

Question 13

What does the notation P(A) mean?

Answer 13

It translates to “Probability of Event A”

Question 14

If A is the event and A’ is the complimentary event, then:

Answer 14

P(A’) = 1 - P(A) OR P(A) + P(A’) = 1

Question 15

What is the formula for the number of expected favorable outcomes of an event?

Answer 15

P(E) * # of attempts

Question 16

How can odds be expressed?

Answer 16

As a fraction or as a ratio, such as 5:1, or 5 to 1.

Question 17

What is the formula for odds in favor of an event?

Answer 17

number of favorable outcomes / number of unfavorable outcomes

Question 18

What is the formula for odds against an event?

Answer 18

number of unfavorable outcomes / number of favorable outcomes

Question 19

After dividing both the numerator and denominator by the total number of possible outcomes of the experiment, odds in favor of an event (E) = …

Answer 19

P(E)/P(E’) = P(E)/[1 - P(E)]

Question 20

If Events A and B are independent (the outcome of Event A does not affect the outcome of Event B), what is the formula for P(A and B)?

Answer 20

P(A) * P(B)

Question 21

If Events A and B are dependent (the outcome of Event A affects the outcome of Event B), what is the formula for P(A and B)?

Answer 21

P(A) * P(B/A)

Question 22

What is the formula for the experimental probability of an event?

Answer 22

number of times the event occurs / number of times the experiment is repeated

Question 23

What is the formula for geometric probability?

Answer 23

P(a point chosen at random is from a particular region) = area of a particular region / total possible area