Q: A county welfare agency employs 10 workers, 3 of whom give illegal deductions. If two workers are randomly selected without replacement, what is the probability both have given illegal deductions?

$$\frac{3}{10} \times \frac{2}{9} = \frac{1}{15}$$

Q: If events A and B are independent, which of the following is always true?

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

Question 1

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

Accepted Answer

The set of all possible outcomes of an experiment.

Question 2

A fair die is rolled. What is the probability of observing an even number?

Accepted Answer

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

Question 3

If two coins are tossed, what is the probability of getting at least one head?

Accepted Answer

$$\frac{3}{4}$$

Question 4

In the AAMFT study, what is the probability that a randomly selected divorced couple is either 'Angry Associates' or 'Fiery Foes'?

Accepted Answer

$$0.25 + 0.25 = 0.50$$

Question 5

Which of the following statements about mutually exclusive events is TRUE?

Accepted Answer

If events A and B are mutually exclusive, $$P(A \cap B) = 0.$$

Question 6

Given the probabilities for the AAMFT survey: $$P(PP) = 0.12$$, $$P(CC) = 0.38$$, $$P(AA) = 0.25$$, $$P(FF) = 0.25. $$What is the probability that a couple has at least some conflict (i.e., is in CC, AA, or FF)?

Accepted Answer

$$0.38 + 0.25 + 0.25 = 0.88$$

Question 7

If $$P(A) = 0.3$$, $$P(B) = 0.1$$, and A and B are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.03$$

Question 8

A sample space consists of five points with probabilities: $$P(1) = 0.05$$, $$P(2) = 0.20$$, $$P(3) = 0.30$$, $$P(4) = 0.30$$, $$P(5) = 0.15. $$What is the probability of the event {1, 2, 3}?

Accepted Answer

$$0.05 + 0.20 + 0.30 = 0.55$$

Question 9

Which formula correctly expresses 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 10

If $$P(A) = 0.7$$, what is $$P(A^c)$$, the probability of the complement of A?

Accepted Answer

$$0.3$$

Question 11

A manufacturer finds that 32% of complaints are about appearance and 63% of complaints occur during the guarantee period. What is the probability that a complaint is about appearance given it occurred during the guarantee period?

Accepted Answer

$$\frac{0.32}{0.63} \approx 0.51$$

Question 12

If three fair coins are tossed, what is the probability of getting at least one head?

Accepted Answer

$$1 - \frac{1}{8} = \frac{7}{8}$$

Question 13

Which of the following is NOT a property of probability for sample points?

Accepted Answer

The probability of a sample point can be negative.

Question 14

A county welfare agency employs 10 workers, 3 of whom give illegal deductions. If two workers are randomly selected without replacement, what is the probability both have given illegal deductions?

Accepted Answer

$$\frac{3}{10} 	imes \frac{2}{9} = \frac{1}{15}$$

Question 15

If $$P(A) = 0.3$$, $$P(B) = 0.1$$, and A and B are independent, what is $$P(A \cup B)$$?

Accepted Answer

$$0.3 + 0.1 - 0.03 = 0.37$$

Question 16

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

Accepted Answer

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

Question 17

If events A and B are independent, which of the following is always true?

Accepted Answer

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

Question 18

A sample space for an experiment is S = {1, 2, 3, 4, 5, 6}. If event A = {2, 4, 6}, what is the complement of A?

Accepted Answer

{1, 3, 5}

Probability: Events, Sample Spaces, and Probability Rules

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