Question

question 6
4 pts
amita pays $0.88 to play a game at a local fair that involves receiving the number of quarters that corresponds to the number that comes up on the roll of a die. using the expected value of the game, compute the expected gain or loss for amita.
note: please avoid rounding numbers in the middle of your calculations. however, round your final answer to two decimal places, before entering it in the box below. a negative final answer indicates an expected loss for amita for playing the game.

Explanation:

Step1: Calculate the expected number of quarters

The probability of rolling each number \(n\) (where \(n = 1,2,\cdots,6\)) on a fair die is \(P(n)=\frac{1}{6}\).
The expected value of the number of quarters \(E(X)\) is given by the formula \(E(X)=\sum_{n = 1}^{6}n\times P(n)\).

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Step2: Calculate the expected value of the money received

Since each quarter is worth \(0.25\) dollars, the expected value of the money received \(E(M)\) is \(E(M)=0.25\times E(X)\).
Substitute \(E(X) = 3.5\) into the formula: \(E(M)=0.25\times3.5 = 0.875\) dollars.

Step3: Calculate the expected gain or loss

The cost to play the game \(C = 0.88\) dollars.
The expected gain or loss \(G\) is \(G=E(M)-C\).
Substitute \(E(M)=0.875\) and \(C = 0.88\) into the formula: \(G=0.875-0.88=- 0.005\approx - 0.01\)

Answer:

\(-0.01\)