Question

you are considering two investment opportunities. for investment a there is a 25% chance that you lose $20,000, a 50% chance that you break even, and a 25% chance that you make $80,000. for investment b there is a 30% chance that you lose $50,000, a 50% chance that you break even, and a 20% chance that you make $180,000. based on the expected value of each, which investment should you make? the expected value of investment a is $ the expected value of investment b is $ based on the expected value, you should make

Explanation:

Step1: Calculate expected value of investment A

The formula for expected value \(E(X)=\sum_{i}x_ip_i\). For investment A: \(x_1 = - 20000\) (loss), \(p_1=0.25\); \(x_2 = 0\) (break - even), \(p_2 = 0.5\); \(x_3=80000\) (profit), \(p_3 = 0.25\).

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Step2: Calculate expected value of investment B

For investment B: \(x_1=-50000\) (loss), \(p_1 = 0.3\); \(x_2 = 0\) (break - even), \(p_2=0.5\); \(x_3 = 180000\) (profit), \(p_3=0.2\)

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Answer:

The expected value of investment A is \(15000\). The expected value of investment B is \(21000\). Based on the expected value, you should make investment B.