Find the expected value.
-The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one:
$5200 (1 chance in 8900); $2500 (1 chance in 6400); $900 (1 chance in 3900); $100 (1 chance in 2100).
Find the expected value of the amount won for one entry if the cost of entering is 57 cents.
A)$100.00
B)$0.62
C)$1.21
D)$0.68

Question

Quizplus · Accepted Answer

The expected value (EV) is calculated by multiplying each prize amount by its probability of winning and summing these products. Subtract the cost of entering (57 cents) from the sum to find the net expected value.- For $5200, the probability is 1/8900, so EV = $5200 * (1/8900).- For $2500, the probability is 1/6400, so EV = $2500 * (1/6400).- For $900, the probability is 1/3900, so EV = $900 * (1/3900).- For $100, the probability is 1/2100, so EV = $100 * (1/2100).Summing these gives the total expected value before the cost of entering:$$EV = \frac{5200}{8900} + \frac{2500}{6400} + \frac{900}{3900} + \frac{100}{2100}$$$$EV \approx 0.58427 + 0.390625 + 0.230769 + 0.047619 = 1.25329$$Subtracting the cost of entering (57 cents or $0.57) from this sum gives the net expected value:$$Net EV = 1.25329 - 0.57 = 0.68329$$Rounded to the nearest cent, the expected value is $0.68.

Find the Expected Value