Question

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?

Answer 1

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

What is the probability?

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

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

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;

First prize × Probability of winning first prize + First prize ×Probability of winning second prize  

→2,000×0.005+500×0.008

→10+4

→14

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

Learn more about Probability :

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