select the correct answer.\nin a radio station contest, the first prize is $2,000 and the second prize is…

select the correct answer.\nin a radio station contest, the first prize is $2,000 and the second prize is $500. the probability of winning the first prize is 0.005 and the probability of winning the second prize is 0.008. the station runs this contest many, many times to increase its listening audience. what is the expected payout for each time the station offers the opportunity to win the prizes?\n\na. $2,300\nb. $500\nc. $100\nd. $14\ne. $10

select the correct answer.\nin a radio station contest, the first prize is $2,000 and the second prize is $500. the probability of winning the first prize is 0.005 and the probability of winning the second prize is 0.008. the station runs this contest many, many times to increase its listening audience. what is the expected payout for each time the station offers the opportunity to win the prizes?\n\na. $2,300\nb. $500\nc. $100\nd. $14\ne. $10

Answer

Explanation:

Step1: Recall expected - value formula

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 values and $p_i$ are their corresponding probabilities. Here, $x_1 = 2000$ (first - prize amount) with probability $p_1=0.005$, and $x_2 = 500$ (second - prize amount) with probability $p_2 = 0.008$.

Step2: Calculate the contribution of the first prize

The contribution of the first prize to the expected value is $x_1p_1=2000\times0.005 = 10$.

Step3: Calculate the contribution of the second prize

The contribution of the second prize to the expected value is $x_2p_2=500\times0.008 = 4$.

Step4: Calculate the expected value

$E(X)=x_1p_1 + x_2p_2=10 + 4=14$.

Answer:

D. $14$