Q1. A very large company has equal amounts of male and female employees. If a random sample of four employees is selected, what is the probability that all four employees selected are female?

A)   0.0256

B)   0.1600

C)   0.0625.

Q2. A joint probability of A and B must always be:

A)   greater than or equal to the conditional probability of A given B.

B)   less than or equal to the conditional probability of A given B.

C)   less than the probability of A and the probability of B.

Q3. Which of the following is a joint probability? The probability that a:

A)     stock pays a dividend and splits next year.

B)     company merges with another firm next year.

C)     stock increases in value after an increase in interest rates has occurred.

答案和详解如下：

Q1. A very large company has equal amounts of male and female employees. If a random sample of four employees is selected, what is the probability that all four employees selected are female?

A)   0.0256

B)   0.1600

C)   0.0625.

Correct answer is C)

Each employee has equal chance of being male or female. Hence, probability of 4 “successes” = (0.5)⁴ = 0.0625

Q2. A joint probability of A and B must always be:

A)   greater than or equal to the conditional probability of A given B.

B)   less than or equal to the conditional probability of A given B.

C)   less than the probability of A and the probability of B.

Correct answer is B)

By the formula for joint probability: P(AB)=P(A|B) × P(B), since P(B) ≤ 1, then P(AB) ≤ P(A|B). Both remaining choices must hold.

Q3. Which of the following is a joint probability? The probability that a:

A)     stock pays a dividend and splits next year.

B)     company merges with another firm next year.

C)     stock increases in value after an increase in interest rates has occurred.

Correct answer is A)

A joint probability applies to two events that both must occur.

Thanks

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