Reading 8: Probability Concepts - LOS i ～ Q1-3 style, black

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1、There is a 90 percent chance that the economy will be good next year and a 10 percent chance that it will be bad. If the economy is good, there is a 60 percent chance that XYZ Incorporated will have EPS of $4.00 and a 40 percent chance that their earnings will be $3.00. If the economy is bad, there is an 80 percent chance that XYZ Incorporated will have EPS of $2.00 and a 20 percent chance that their earnings will be $1.00. What is the firm’s expected EPS?

A)   $2.50.

B)   $5.40.

C)   $2.93.

D)   $3.42.

2、There is an 80 percent chance that the economy will be good next year and a 20 percent chance that it will be bad. If the economy is good, there is a 60 percent chance that XYZ Incorporated will have EPS of $3.00 and a 40 percent chance that their earnings will be $2.50. If the economy is bad, there is a 70 percent chance that XYZ Incorporated will have EPS of $1.50 and a 30 percent chance that their earnings will be $1.00. What is the firm’s expected EPS?

A)   $2.00.

B)   $4.16.

C)   $2.51.

D)   $1.85.

3、There is a 60 percent chance that the economy will be good next year and a 40 percent chance that it will be bad. If the economy is good, there is a 70 percent chance that XYZ Incorporated will have EPS of $5.00 and a 30 percent chance that their earnings will be $3.50. If the economy is bad, there is an 80 percent chance that XYZ Incorporated will have EPS of $1.50 and a 20 percent chance that their earnings will be $1.00. What is the firm’s expected EPS?

A)   $2.75.

B)   $5.95.

C)   $3.29.

D)   $1.86.

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答案和详解如下：

1、There is a 90 percent chance that the economy will be good next year and a 10 percent chance that it will be bad. If the economy is good, there is a 60 percent chance that XYZ Incorporated will have EPS of $4.00 and a 40 percent chance that their earnings will be $3.00. If the economy is bad, there is an 80 percent chance that XYZ Incorporated will have EPS of $2.00 and a 20 percent chance that their earnings will be $1.00. What is the firm’s expected EPS?

A)   $2.50.

B)   $5.40.

C)   $2.93.

D)   $3.42.

The correct answer was D)

The expected EPS is calculated by multiplying the probability of the economic environment by the probability of the particular EPS and the EPS in each case. The expected EPS in all four outcomes are then summed to arrive at the expected EPS: (0.90 × 0.60 × $4.00) + (0.90 × 0.40 × $3.00) +(0.10 × 0.80 × $2.00) +(0.10 × 0.20 × $1.00) = $2.16 + $1.08 + $0.16 + $0.02 = $3.42.

2、There is an 80 percent chance that the economy will be good next year and a 20 percent chance that it will be bad. If the economy is good, there is a 60 percent chance that XYZ Incorporated will have EPS of $3.00 and a 40 percent chance that their earnings will be $2.50. If the economy is bad, there is a 70 percent chance that XYZ Incorporated will have EPS of $1.50 and a 30 percent chance that their earnings will be $1.00. What is the firm’s expected EPS?

A)   $2.00.

B)   $4.16.

C)   $2.51.

D)   $1.85.

The correct answer was C)

The expected EPS is calculated by multiplying the probability of the economic environment by the probability of the particular EPS and the EPS in each case. The expected EPS in all four outcomes are then summed to arrive at the expected EPS: (0.80 × 0.60 × $3.00) + (0.80 × 0.40 × $2.50) + (0.20 × 0.70 × $1.50) +(0.20 × 0.30 × $1.00) = $1.44 + $0.80 + $0.21 + $0.06 = $2.51.

3、There is a 60 percent chance that the economy will be good next year and a 40 percent chance that it will be bad. If the economy is good, there is a 70 percent chance that XYZ Incorporated will have EPS of $5.00 and a 30 percent chance that their earnings will be $3.50. If the economy is bad, there is an 80 percent chance that XYZ Incorporated will have EPS of $1.50 and a 20 percent chance that their earnings will be $1.00. What is the firm’s expected EPS?

A)   $2.75.

B)   $5.95.

C)   $3.29.

D)   $1.86.

The correct answer was C)

The expected EPS is calculated by multiplying the probability of the economic environment by the probability of the particular EPS and the EPS in each case. The expected EPS in all four outcomes are then summed to arrive at the expected EPS: (0.60 × 0.70 × $5.00) + (0.60 × 0.30 × $3.50) +(0.40 × 0.80 × $1.50) +(0.40 × 0.20 × $1.00) = $2.10 + $0.63 + $0.48 + $0.08 = $3.29.