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Jessica is playing a game where there are 4 blue markers and 6 red markers in a box. She is going to pick 3 markers without replacement.

If she picks all 3 red markers, she will win a total of $500. If  the first marker she picks is red but not all 3 markers are red, she will win a total of $100. Under any other outcome, she will win $0.

What is the expected value of Jessica's winnings?

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$P (\text{All red})$ = $\large \frac{6}{10} \times \frac{5}{9} \times \frac{4}{8} = 0.166$

$P (\text{1st red but not all})$ = $P(\text{1st red}) -$ $P (\text{All red})$ = $\large \frac{6}{10} $$- 0.166 = 0.434$

$E[X] = \sum_{x: P(x)>0}^{} x{P(x)}$

$E[X] = 0.166(500) + 0.434(100) + 0.4(0) =126.4 $
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