1215

An analyst has a list of 20 bonds of which 14 are callable, and five have warrants attached to them. Two of the callable bonds have warrants attached to them. If a single bond is chosen at random, what is the probability of choosing a callable bond or a bond with a warrant?

A) 0.70.

B) 0.85.

C) 0.55.

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This requires the addition formula, P(callable) + P(warrants) – P(callable and warrants) = P(callable or warrants) = 14/20 + 5/20 – 2/20 = 17/20 = 0.85.

1215

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.

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

1215

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.

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

1215

There is a 30% probability of rain this afternoon. There is a 10% probability of having an umbrella if it rains. What is the chance of it raining and having an umbrella?

A) 3%.

B) 40%.

C) 33%.

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P(A) = 0.30. P(B | A) = 0.10. P(AB) = (0.30)(0.10) = 0.03 or 3%.

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1215

A bond portfolio consists of four BB-rated bonds. Each has a probability of default of 24% and these probabilities are independent. What are the probabilities of all the bonds defaulting and the probability of all the bonds not defaulting, respectively?

A) 0.96000; 0.04000.

B) 0.04000; 0.96000.

C) 0.00332; 0.33360.

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For the four independent events where the probability is the same for each, the probability of all defaulting is (0.24)⁴. The probability of all not defaulting is (1 ? 0.24)⁴.

1215

If two fair coins are flipped and two fair six-sided dice are rolled, all at the same time, what is the probability of ending up with two heads (on the coins) and two sixes (on the dice)?

A) 0.0069.

B) 0.8333.

C) 0.4167.

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For the four independent events defined here, the probability of the specified outcome is 0.5000 × 0.5000 × 0.1667 × 0.1667 = 0.0069.

1215

If two events are independent, the probability that they both will occur is:

A) 0.50.

B) Cannot be determined from the information given.

C) 0.00.

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If two events are independent, their probability of their joint occurrence is computed as follows:  P(A∩B) = P(A) × P(B). Since we are not given any information on the respective probabilities of A or B, there is not enough information.

1215

A very large company has twice as many male employees relative to female employees. If a random sample of four employees is selected, what is the probability that all four employees selected are female?

A) 0.0123.

B) 0.3333.

C) 0.0625.

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Since there are twice as many male employees to female employees, P(male) = 2/3 and P(female) = 1/3. Therefore, the probability of 4 “successes” = (0.333)⁴ = 0.0123.