Question

a contest at a fast - food restaurant offered the following cash prizes and probabilities of winning on one visit when a customer buys an order of french fries for $1.69. find the expected winnings if the player buys 25 orders of french fries in multiple visits.

what are the expected winnings if the player buys 25 orders of french fries on multiple visits?
$\square$
(round the final answer to the nearest cent as needed. round all intermediate values to the nearest cent as needed.)

Explanation:

Step1: Calculate the expected value for one visit

The formula for the expected value \(E(X)\) is \(E(X)=\sum_{i}x_ip_i\), where \(x_i\) is the prize amount and \(p_i\) is the probability of winning that prize.

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$$ E(X)\approx0.01176 + 0.1653+0.03537+0.00651+0.00096+0.00262\approx0.2225 $$

Step2: Calculate the expected value for 25 visits

If the expected value for one visit is \(E(X)\approx0.2225\), then for \(n = 25\) visits, the expected value \(E = n\times E(X)\)
\(E=25\times0.2225 = 5.5625\approx5.56\)

Answer:

\(5.56\)