Q: A probability experiment consists of tossing a coin and spinning a spinner with numbers 1, 2, 3, and 4. What is the probability of tossing a tail and spinning an odd number?

$$\frac{1}{2} \times \frac{2}{4} = \frac{1}{4}$$

Q: A coin is tossed and a die is rolled. What is the probability of getting a head and then rolling a 6?

$$\frac{1}{2} \times \frac{1}{6} = \frac{1}{12}$$

Q: The probability that a knee surgery is successful is $$0.85. $$What is the probability that three knee surgeries are all successful?

$$0.85 \times 0.85 \times 0.85 = 0.614125$$

Q: If events A and B are mutually exclusive, what is the probability that A or B will occur?

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

Question 1

Which of the following best describes the sample space for a probability experiment consisting of rolling a six-sided die?

Accepted Answer

The set of all possible numbers from 1 to 6: $$\{1, 2, 3, 4, 5, 6\}$$

Question 2

A probability experiment consists of rolling a die and flipping a coin. How many outcomes are in the sample space?

Accepted Answer

$$12$$

Question 3

You roll a six-sided die. Event B is rolling at least a 4. Is this a simple event?

Accepted Answer

No, because it consists of multiple outcomes: $$\{4, 5, 6\}$$

Question 4

Using the Fundamental Counting Principle, how many different ways can you select one manufacturer, one car size, and one color if there are 3 manufacturers, 2 car sizes, and 4 colors?

Accepted Answer

$$3 	imes 2 	imes 4 = 24$$

Question 5

What is the probability of rolling at least 5 on a six-sided die?

Accepted Answer

$$\frac{2}{6} = \frac{1}{3}$$

Question 6

What is the probability of drawing a Jack out of a standard deck of 52 cards?

Accepted Answer

$$\frac{4}{52} = \frac{1}{13}$$

Question 7

If $$P(E) = 0.3$$, what is the probability of the complement event $$E'$$?

Accepted Answer

$$P(E') = 1 - P(E) = 0.7$$

Question 8

A survey of 1000 employees records their ages. What is the probability of randomly choosing an employee who is not between 25 and 34 years old?

Accepted Answer

$$P(E') = 1 - \frac{366}{1000} = 0.634$$

Question 9

A probability experiment consists of tossing a coin and spinning a spinner with numbers 1, 2, 3, and 4. What is the probability of tossing a tail and spinning an odd number?

Accepted Answer

$$\frac{1}{2} 	imes \frac{2}{4} = \frac{1}{4}$$

Question 10

Two cards are selected in sequence from a standard deck. What is the probability that the second card is a queen, given that the first card is a king (not replaced)?

Accepted Answer

$$\frac{4}{51}$$

Question 11

In a study, 33 children with a specific gene have high IQ. If 72 children have the gene, what is the probability that a child with the gene has a high IQ?

Accepted Answer

$$\frac{33}{72}$$

Question 12

Are the events 'selecting a king from a deck, not replacing it, then selecting a queen' independent or dependent?

Accepted Answer

Dependent, because the first selection affects the second

Question 13

A coin is tossed and a die is rolled. What is the probability of getting a head and then rolling a 6?

Accepted Answer

$$\frac{1}{2} 	imes \frac{1}{6} = \frac{1}{12}$$

Question 14

The probability that a knee surgery is successful is $$0.85. $$What is the probability that three knee surgeries are all successful?

Accepted Answer

$$0.85 	imes 0.85 	imes 0.85 = 0.614125$$

Question 15

If events A and B are mutually exclusive, what is the probability that A or B will occur?

Accepted Answer

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

Question 16

You select a card from a standard deck. What is the probability that the card is a 4 or an ace?

Accepted Answer

$$\frac{8}{52} = \frac{2}{13}$$

Question 17

How many distinguishable ways can a contractor plant 6 oak, 9 maple, and 5 poplar trees along a street?

Accepted Answer

$$\frac{20!}{6!\ 9!\ 5!}$$

Question 18

The manager of an accounting department wants to form a three-person advisory committee from 20 employees. In how many ways can this committee be formed?

Accepted Answer

$$\frac{20!}{(20-3)!\ 3!} = 1140$$

Question 19

Refer to the Mega Millions lottery image. Five numbers are chosen from 1 to 56 and one Mega Ball from 1 to 46. What is the probability of winning the jackpot with one ticket?

Accepted Answer

$$\frac{1}{\binom{56}{5} 	imes 46}$$

Question 20

A food manufacturer analyzes a sample of 400 corn kernels, 3 of which have dangerously high toxin levels. If 4 kernels are randomly selected, what is the probability that exactly one kernel contains a dangerously high level of toxin?

Accepted Answer

$$\binom{4}{1} 	imes \frac{3}{400} 	imes \left(\frac{397}{400}\$$right)^3$$

Probability: Concepts, Rules, and Counting Principles

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