Q: Which of the following statements is true for independent events A and B?

$$P(A \cap B) = P(A) \times P(B)$$

Q: A box contains 3 green, 2 blue, and 5 red marbles. If two marbles are drawn without replacement, what is the probability that both are blue?

$$\frac{2}{10} \times \frac{1}{9} = \frac{2}{90}$$

Q: A medical test for a disease has a 95% chance of detecting the disease when it is present (true positive) and a 5% chance of a false positive. If 1% of the population has the disease, what is the probability that a randomly selected person tests positive?

$$0.01 \times 0.95 + 0.99 \times 0.05 = 0.059$$

Q: A company has 14 blue pens and 6 red pens. If two pens are selected without replacement, what is the probability that both are red?

$$\frac{6}{20} \times \frac{5}{19} = \frac{3}{38}$$

Question 1

Which of the following best describes a sample space in probability theory?

Accepted Answer

A collection of all possible outcomes of an experiment.

Question 2

If you toss a fair coin twice, what is the probability of getting exactly one head?

Accepted Answer

$$\frac{1}{2}$$

Question 3

Given a deck of 52 cards, what is the probability of drawing either an Ace or a Black card?

Accepted Answer

$$\frac{28}{52}$$

Question 4

Which formula correctly represents the probability of the union of two events A and B?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Question 5

If events A and B are mutually exclusive, which of the following is true?

Accepted Answer

$$P(A \cap B) = 0$$

Question 6

A bag contains 5 red balls and 7 blue balls. If one ball is drawn at random, what is the probability that it is not red?

Accepted Answer

$$\frac{7}{12}$$

Question 7

Which of the following is the correct formula for conditional probability?

Accepted Answer

$$P(A|B) = \frac{P(A \cap B)}{P(B)}$$

Question 8

If $$P(A) = 0.6$$ and $$P(A^C) is $$the probability of the complement of A, what is $$P(A^C)$$?

Accepted Answer

$$0.4$$

Question 9

A factory inspects 10 parts and finds 6 are of type A and 4 are of type B. If 5 parts are defective and 5 are not, what is the probability that a randomly selected part is both type B and defective, given that 1 part is both type B and defective?

Accepted Answer

$$\frac{1}{10}$$

Question 10

Which of the following statements is true for independent events A and B?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Question 11

A box contains 3 green, 2 blue, and 5 red marbles. If two marbles are drawn without replacement, what is the probability that both are blue?

Accepted Answer

$$\frac{2}{10} 	imes \frac{1}{9} = \frac{2}{90}$$

Question 12

If $$P(A) = 0.7$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.4$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.8$$

Question 13

Which of the following is NOT a property of probability?

Accepted Answer

The probability of any event is always negative.

Question 14

A committee of 3 is to be chosen from 8 people. How many different committees are possible?

Accepted Answer

$$\frac{8!}{3!5!} = 56$$

Question 15

If $$P(A|B) = 0.3$$ and $$P(B) = 0.5$$, what is $$P(A \cap B)$$?

Accepted Answer

$$0.15$$

Question 16

A medical test for a disease has a 95% chance of detecting the disease when it is present (true positive) and a 5% chance of a false positive. If 1% of the population has the disease, what is the probability that a randomly selected person tests positive?

Accepted Answer

$$0.01 	imes 0.95 + 0.99 	imes 0.05 = 0.059$$

Question 17

If $$P(A) = 0.3$$, $$P(B) = 0.4$$, and A and B are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.7$$

Question 18

Which of the following best describes the complement of an event A?

Accepted Answer

All outcomes in the sample space that are not in A.

Question 19

If two events are independent, which of the following must be true?

Accepted Answer

$$P(A|B) = P(A)$$

Question 20

A company has 14 blue pens and 6 red pens. If two pens are selected without replacement, what is the probability that both are red?

Accepted Answer

$$\frac{6}{20} 	imes \frac{5}{19} = \frac{3}{38}$$

Probability: Events, Sample Spaces, and Probability Rules

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