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# Both situations have the same expected value. Find the missing information. Situation 1: Paul hits a dart target worth 15 points 45% of the time. Situation 2: He hits a dart target worth 10 points x% of the time.

Solution

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Use the expected value formula:

$E(x)=x_1P(x_1)+ x_2P(x_2)+ x_3P(x_3)+\cdots+ x_nP(x_n)\color{white}{\tag{1}}$

Since the expected values are the same, then we can write:

$E_1=E_2$

$15\cdot \dfrac{45}{100}=10\cdot \dfrac{x}{100}$

Mutliply both sides by 100:

$15\cdot 45=10x$

$675=10x$

$67.5=x$

The missing information is $\color{#c34632}{67.5\%}$.

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