Probability

Question 1

What is the probability of an event?

Answer 1

The probability of an event is a measure of the likelihood that the event will occur, calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Question 2

True or False: The probability of an event can be greater than 1.

Answer 2

False

Question 3

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

Answer 3

P(E) = Number of favorable outcomes / Total number of possible outcomes

Question 4

Fill in the blank: The sum of the probabilities of all possible outcomes of a random experiment is _____ .

Answer 4

1

Question 5

If a fair six-sided die is rolled, what is the probability of rolling a 3?

Answer 5

1/6

Question 6

What is the probability of flipping a fair coin and getting heads?

Answer 6

1/2

Question 7

True or False: The probability of an impossible event is 0.

Answer 7

True

Question 8

What is the complement of an event?

Answer 8

The complement of an event is the set of outcomes in which the event does not occur.

Question 9

If the probability of event A is 0.3, what is the probability of the complement of A?

Answer 9

0.7

Question 10

What is a sample space?

Answer 10

A sample space is the set of all possible outcomes of a random experiment.

Question 11

In a standard deck of cards, what is the probability of drawing a heart?

Answer 11

1/4

Question 12

What is the formula for the probability of the union of two events A and B?

Answer 12

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Question 13

True or False: Two events are independent if the occurrence of one does not affect the probability of the other.

Answer 13

True

Question 14

What is the probability of drawing a spade or a heart from a standard deck of cards?

Answer 14

1/2

Question 15

Fill in the blank: The probability of two independent events A and B occurring together is _____ .

Answer 15

P(A) * P(B)

Question 16

What does it mean if two events are mutually exclusive?

Answer 16

It means that the two events cannot occur at the same time.

Question 17

If a bag contains 3 red balls and 2 blue balls, what is the probability of randomly selecting a red ball?

Answer 17

3/5

Question 18

What is the expected value in probability?

Answer 18

The expected value is the average of all possible outcomes, weighted by their probabilities.

Question 19

What is the probability of drawing an Ace from a standard deck of cards?

Answer 19

4/52 or 1/13

Question 20

True or False: A probability of 0.5 indicates an equal chance of an event occurring or not occurring.

Answer 20

True

Question 21

What is a discrete probability distribution?

Answer 21

A discrete probability distribution describes the probabilities of the outcomes of a discrete random variable.

Question 22

What is the probability of rolling an even number on a fair six-sided die?

Answer 22

3/6 or 1/2

Question 23

Fill in the blank: The Law of Large Numbers states that as the number of trials increases, the experimental probability will get closer to the _____ .

Answer 23

theoretical probability

Question 24

What is the difference between theoretical and experimental probability?

Answer 24

Theoretical probability is based on the expected outcomes, while experimental probability is based on actual trials.

Question 25

If two dice are rolled, what is the probability of getting a sum of 7?

Answer 25

6/36 or 1/6

Question 26

What is a continuous probability distribution?

Answer 26

A continuous probability distribution describes the probabilities of the outcomes of a continuous random variable.