At 7-11, I get my change from a Slurpee in all nickels and pennies. If I get $0.87 in change, and a total of 31 coins, how many
1 answer:
Given:
The change all in nickels and pennies.
Let the number of nickels = x
Let the number of pennies = y
Total coins = 31
so, x + y = 31
1 nickel = 5 cents
1 penny = 1 cent
The change = $0.87 = 87 cents
so, 5x + y = 87
so, we have the following system of equations:
So, the number of nickels = x = 14
And the number of pennies = y = 17
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The game is not fair as 6 times the expected sum is less than the cost, $43.
In the question, we are asked if the game is fair.
For the game to be fair, 6 times the expected sum for the pair from the game has to be greater than or equal to $43, that is,
6E(X) ≥ 43.
The expected sum for the pair, E(X) can be calculated using the formula,
E(X) = ∑x.p(x),
or, E(X) = 1/18 + 1/6 + 1/3 + 5/9 + 1/6 + 7/9 + 10/9 + 1 + 5/6 + 11/18 + 1/3,
or, E(X) = 107/18.
Now, 6E(X) = 6*(107/18) = 107/3 = 35.67.
Since, the total return from the game is $35.67, which is less than the cost of $43, the game is not fair.
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