Q: Suppose a bag contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is not blue?

$$P(\text{not blue}) = 1 - \frac{3}{10} = 0.7$$

Q: If two events E and F are disjoint, which formula correctly gives the probability of E or F occurring?

$$P(E \text{ or } F) = P(E) + P(F)$$

Q: Suppose the probability that a randomly selected American has played a state lottery is 0.52. What is the probability that a randomly selected American has NOT played a state lottery?

$$P(\text{not played}) = 1 - 0.52 = 0.48$$

Q: In a game of roulette, the probability that the ball lands on 21 in a single spin is $$\frac{1}{38}. $$What is the probability that the ball lands on 21 in two consecutive spins?

$$P = \frac{1}{38} \times \frac{1}{38} = \frac{1}{1444}$$

Q: A shipment of 120 fasteners contains 4 defective fasteners. If 5 fasteners are randomly selected, what is the probability that exactly 1 is defective?

$$P = \frac{\binom{4}{1} \times \binom{116}{4}}{\binom{120}{5}}$$

Q: A committee of 3 men and 2 women is to be formed from 5 men and 4 women. How many different subcommittees are possible?

$$\binom{5}{3} \times \binom{4}{2} = 10 \times 6 = 60$$

Question 1

Which of the following best describes the Law of Large Numbers?

Accepted Answer

As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome.

Question 2

A probability experiment consists of rolling a fair six-sided die. What is the probability of rolling an even number using the classical method?

Accepted Answer

$$P(E) = \frac{3}{6} = 0.5$$

Question 3

Suppose a bag contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is not blue?

Accepted Answer

$$P(	ext{not blue}) = 1 - \frac{3}{10} = 0.7$$

Question 4

Which of the following is an example of a subjective probability?

Accepted Answer

A sports reporter predicts there is a 20% chance the Red Sox will play in the World Series.

Question 5

If two events E and F are disjoint, which formula correctly gives the probability of E or F occurring?

Accepted Answer

$$P(E 	ext{ or } F) = P(E) + P(F)$$

Question 6

A card is drawn from a standard deck. What is the probability of drawing a king or a queen or a jack?

Accepted Answer

$$P = \frac{4 + 4 + 4}{52} = \frac{12}{52} = 0.231$$

Question 7

Suppose the probability that a randomly selected American has played a state lottery is 0.52. What is the probability that a randomly selected American has NOT played a state lottery?

Accepted Answer

$$P(	ext{not played}) = 1 - 0.52 = 0.48$$

Question 8

Which of the following statements is TRUE regarding independent and disjoint events?

Accepted Answer

If two events are disjoint, they are not independent.

Question 9

In a game of roulette, the probability that the ball lands on 21 in a single spin is $$\frac{1}{38}. $$What is the probability that the ball lands on 21 in two consecutive spins?

Accepted Answer

$$P = \frac{1}{38} 	imes \frac{1}{38} = \frac{1}{1444}$$

Question 10

Suppose the probability that a randomly selected 24-year-old male survives the year is 0.9986. What is the probability that all three randomly selected 24-year-old males survive the year?

Accepted Answer

$$P = 0.9986^3$ = 0.9958$$

Question 11

A shipment of 120 fasteners contains 4 defective fasteners. If 5 fasteners are randomly selected, what is the probability that exactly 1 is defective?

Accepted Answer

$$P = \frac{\binom{4}{1} 	imes \binom{116}{4}}{\binom{120}{5}}$$

Question 12

How many distinguishable DNA sequences can be formed using two A's, two C's, three G's, and one T?

Accepted Answer

$$\frac{8!}{2!2!3!1!} = 1680$$

Question 13

A committee of 3 men and 2 women is to be formed from 5 men and 4 women. How many different subcommittees are possible?

Accepted Answer

$$\binom{5}{3} 	imes \binom{4}{2} = 10 	imes 6 = 60$$

Question 14

Which formula would you use to compute the probability that a randomly selected U.S. resident is male or widowed, given that there are males who are widowed?

Accepted Answer

$$P(	ext{male or widowed}) = P(	ext{male}) + P(	ext{widowed}) - P(	ext{male and widowed})$$

Question 15

If the probability that a driver who is speeding gets pulled over is 0.8, and the probability that a driver gets a ticket given they are pulled over is 0.9, what is the probability that a speeding driver gets pulled over and gets a ticket?

Accepted Answer

$$P = 0.8 	imes 0.9 = 0.72$$

Question 16

How many different ways can the top four finishers in a 43-driver race be arranged?

Accepted Answer

$$P(43,4) = \frac{43!}{(43-4)!} = 2,961,840$$

Question 17

Which of the following best describes a simulation in probability?

Accepted Answer

A technique used to re-create a random event, either physically or virtually, to measure how often a certain outcome is observed.

Probability and Counting Techniques in Statistics

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