Question

a person randomly selects one of six envelopes. each envelope contains a check that the person gets to keep. determine the persons expectation if three envelopes contain a $498 check and three envelopes contain a $978 check. the expected value is $ (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Calculate the probability of each outcome

The probability of selecting a $498$ check is $P(498)=\frac{3}{6}=\frac{1}{2}$.
The probability of selecting a $978$ check is $P(978)=\frac{3}{6}=\frac{1}{2}$.

Step2: Use the expected - value formula

The expected - value formula is $E(X)=\sum_{i}x_{i}P(x_{i})$.
Here, $x_1 = 498$, $P(x_1)=\frac{1}{2}$ and $x_2 = 978$, $P(x_2)=\frac{1}{2}$.
So, $E(X)=498\times\frac{1}{2}+978\times\frac{1}{2}$.

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Answer:

$738$