you are considering two investment opportunities. for investment a there is a 25% chance that you lose…

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 $______.

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 $______.

Answer

Explanation:

Step1: Define the formula for expected value

The formula for the expected value $E(X)$ of a discrete - random variable is $E(X)=\sum_{i}x_ip_i$, where $x_i$ are the possible outcomes and $p_i$ are their corresponding probabilities.

Step2: Identify the outcomes and probabilities for investment A

For investment A, $x_1=- 20000$ (a loss of $20000$) with probability $p_1 = 0.25$, $x_2 = 0$ (break - even) with probability $p_2=0.5$, and $x_3 = 80000$ (a gain of $80000$) with probability $p_3 = 0.25$.

Step3: Calculate the expected value of investment A

$E(A)=x_1p_1 + x_2p_2+x_3p_3$ $E(A)=(-20000)\times0.25+0\times0.5 + 80000\times0.25$ $E(A)=-5000 + 0+20000$ $E(A)=15000$

Answer:

$15000$