In 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?
$2,300
$500
$100
$14
$10

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lclaytor1217 lclaytor1217 · Answer 1 · 2017-03-10T20:15:51+01:00

I think the answer is $14

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psm22415 psm22415 · Answer 2 · 2022-05-17T14:01:48+02:00

The expected payout for each time the station offers the opportunity to win the prizes is $14.

Probability is defined as the sum of all data and the number of all the data.

In 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.

The expected payout for each time the station offers the opportunity to win the prizes is;

[tex]\rm = First prize \times Proabbility\ of \ winning \ first \ prize + First \ prize \times Proabbility \ of\ winning \ second \ prize[/tex]

[tex]\rm = 2,000 \times 0.005 + 500 \times 0.008 \\\\= 10 + 4 \\ \\ =14[/tex]

Hence, The expected payout for each time the station offers the opportunity to win the prizes is $14.

Learn more about probability here;

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