choosing an investment\nyou are considering two investment opportunities. for investment a there is a 25%…

choosing an investment\nyou 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?\nthe expected value of investment a is $\nthe expected value of investment b is $\nbased on the expected value, you should make

choosing an investment\nyou 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?\nthe expected value of investment a is $\nthe expected value of investment b is $\nbased on the expected value, you should make

Answer

Explanation:

Step1: Calculate expected - value of investment A

The formula for expected value $E(X)=\sum_{i}x_ip_i$. For investment A, losing $20000$ means $x_1=- 20000$ with $p_1 = 0.25$, breaking - even means $x_2 = 0$ with $p_2=0.5$, and making $80000$ means $x_3 = 80000$ with $p_3 = 0.25$. $E(A)=(-20000)\times0.25+0\times0.5 + 80000\times0.25$ $E(A)=-5000 + 0+20000$ $E(A)=15000$

Step2: Calculate expected - value of investment B

For investment B, losing $50000$ means $x_1=-50000$ with $p_1 = 0.3$, breaking - even means $x_2 = 0$ with $p_2 = 0.5$, and making $180000$ means $x_3 = 180000$ with $p_3=0.2$. $E(B)=(-50000)\times0.3+0\times0.5+180000\times0.2$ $E(B)=-15000 + 0 + 36000$ $E(B)=21000$

Step3: Compare expected values

Since $E(B)=21000$ and $E(A)=15000$, and $21000>15000$.

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.