Question

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.

Answer 1

The expected value of the amount won after one entry in the sweepstakes, after accounting for the cost of entering, is $0.683283. This is calculated by multiplying the prize amounts by their probabilities of being won and adding these values together, then subtracting the entry cost.

Step-by-step explanation:

The expected value of the amount won in the given sweepstakes can be calculated by multiplying the amount of each prize by the probability of winning that prize and then summing these values. We subtract the cost of entering (57 cents) at the end to find the net expected value.

Expected Value (E) calculation:

• E($5200) = $5200 * (1/8900) = $0.58427
• E($2500) = $2500 * (1/6400) = $0.390625
• E($900) = $900 * (1/3900) = $0.230769
• E($100) = $100 * (1/2100) = $0.047619

Adding these together:

Expected Value (Total) = $0.58427 + $0.390625 + $0.230769 + $0.047619 = $1.253283

Now, we subtract the cost of entering (57 cents) from the total expected value:

Expected Net Value = $1.253283 - $0.57 = $0.683283

Thus, the expected value for entering this sweepstakes after accounting for the cost is $0.68, rounded to the nearest cent.

Answer 2

$0.68

Step-by-step explanation:

Multiply each possible prize by its likelihood and add the results in order to obtain the expected value (Note that there is a 100% of losing 0.57 cents since that is the cost of entry):

`EV = 5200*(1)/(8900) +2500*(1)/(6400) +900*(1)/(3900)+100*(1)/(2100) -0.57*1\\EV= \$0.68`

The expected value of the amount won for one entry if the cost of entering is 57 cents is $0.68