an oil company is considering two sites on wh...
an oil company is considering two sites on which to drill, described as follows: site a: profit if oil is found: $110 million loss if no oil is found: $17 million probability of finding oil: 0.2 site b: profit if oil is found: $165 million loss if no oil is found: $29 million probability of finding oil: 0.1 a. which site has the larger expected profit? site a has the larger expected profit. site b has the larger expected profit. the expected profits for both sites are the same.
Answer
# Explanation:
## Step1: Calculate expected profit for Site A
The expected - value formula for a discrete random variable is $E(X)=p_1x_1 + p_2x_2$, where $p_1$ and $p_2$ are probabilities and $x_1$ and $x_2$ are the corresponding values. For Site A, let $p_1 = 0.2$ (probability of finding oil) and $x_1=110$ (profit if oil is found), $p_2 = 1 - 0.2=0.8$ (probability of no - oil) and $x_2=-17$ (loss if no oil is found). Then $E_A=0.2\times110+0.8\times(-17)$.
$E_A = 22-13.6=8.4$ million.
## Step2: Calculate expected profit for Site B
For Site B, let $p_1 = 0.1$ (probability of finding oil) and $x_1 = 165$ (profit if oil is found), $p_2=1 - 0.1 = 0.9$ (probability of no - oil) and $x_2=-29$ (loss if no oil is found). Then $E_B=0.1\times165+0.9\times(-29)$.
$E_B=16.5 - 26.1=-9.6$ million.
# Answer:
Site A has the larger expected profit.