Q: Which of the following is the correct formula for the probability of the union of two events A and B?

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

Q: A box contains 3 red tokens, 4 yellow tokens, and 5 green tokens. If two tokens are selected without replacement, what is the probability of selecting a red token and then a yellow token?

$$\dfrac{3}{12} \times \dfrac{4}{11}$$

Question 1

Which of the following best describes the Rare Event Rule for Inferential Statistics?

Accepted Answer

If, under a given assumption, the probability of an observed event is extremely small, then the assumption is probably not correct.

Question 2

A password consists of five capital letters, each used only once. How many different passwords can be formed?

Accepted Answer

$$\dfrac{26!}{21!}$$

Question 3

What is the probability of rolling a 2 with one roll of a fair six-sided die?

Accepted Answer

$$\dfrac{1}{6}$$

Question 4

If you flip a coin, spin a spinner with red, green, and blue areas, and then flip another coin, how many possible outcomes are there?

Accepted Answer

$$2 	imes 3 	imes 2 = 12$$

Question 5

Which of the following numbers cannot be a probability?

Accepted Answer

$$-0.2$$

Question 6

A bag contains 5 marbles, 2 of which are red. What is the probability of NOT picking a red marble at random?

Accepted Answer

$$\dfrac{3}{5}$$

Question 7

Which of the following best describes disjoint (mutually exclusive) events?

Accepted Answer

Events that cannot occur at the same time.

Question 8

If you roll a fair 8-sided die, what is the probability of rolling a 4 or an even number?

Accepted Answer

$$\dfrac{5}{8}$$

Question 9

Which of the following is the correct formula for the probability of the union of two events A and B?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B)$$

Question 10

A box contains 3 red tokens, 4 yellow tokens, and 5 green tokens. If two tokens are selected without replacement, what is the probability of selecting a red token and then a yellow token?

Accepted Answer

$$\dfrac{3}{12} 	imes \dfrac{4}{11}$$

Question 11

If one person is randomly selected from a group of 98 people, 39 of whom have blood group A, what is the probability that the person has blood group A?

Accepted Answer

$$\dfrac{39}{98}$$

Question 12

If you roll a 12-sided die, what is the probability of getting a number greater than 3?

Accepted Answer

$$\dfrac{9}{12}$$

Question 13

Which of the following best describes independent events?

Accepted Answer

The occurrence of one event does not affect the probability of the other.

Question 14

A standard deck of cards has 52 cards. What is the probability of drawing an ace or a heart?

Accepted Answer

$$\dfrac{16}{52}$$

Question 15

If $$n!$$ denotes the factorial of $$n$$, what is the value of $$5!$$?

Accepted Answer

$$120$$

Question 16

A box contains 20 tokens numbered 1 to 20. Tokens 1 through 10 are blue. What is the probability of randomly selecting a token with an odd number given that it is blue?

Accepted Answer

$$\dfrac{5}{10}$$

Question 17

If you roll a 6-sided die twice, what is the probability of getting a 3 and then a 4?

Accepted Answer

$$\dfrac{1}{36}$$

Question 18

If one person is randomly selected from a group of 98 people, 6 of whom have blood group AB and are Rh+, what is the probability that the person has blood group AB and is Rh+?

Accepted Answer

$$\dfrac{6}{98}$$

Question 19

If one person is randomly selected from a group of 98 people, 30 of whom have blood group A and are Rh+, and 39 have blood group A, what is the probability that the person is Rh+, given that they have blood group A?

Accepted Answer

$$\dfrac{30}{39}$$

Question 20

Which of the following statements about the Law of Large Numbers is correct?

Accepted Answer

As a procedure is repeated, the relative frequency probability of an event will approach the actual probability.

Chapter 4: Probability – Foundations and Applications in Statistics

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