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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.

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Answer:

$0.68

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):

[tex]EV = 5200*\frac{1}{8900} +2500*\frac{1}{6400} +900*\frac{1}{3900}+100*\frac{1}{2100} -0.57*1\\EV= \$0.68[/tex]

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

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