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uysha [10]
2 years ago
7

If you draw a card with a value of three or less from a standard deck of cards, I will pay you $43. If not, you pay me $11. (Ace

s are considered the highest card in the deck.) Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.
Mathematics
1 answer:
valina [46]2 years ago
3 0

If W is a random variable representing your winnings from playing the game, then it has support

W=\begin{cases}43&\text{if you draw something with value at most 3}\\-11&\text{otherwise}\end{cases}

There are 52 cards in the deck. Only the 1s, 2s, and 3s fulfill the first condition, so there are 12 ways in which you can win $43. So W has PMF

P(W=w)=\begin{cases}\frac{12}{52}=\frac3{13}&\text{for }w=43\\1-\frac{12}{52}=\frac{10}{13}&\text{for }w=-11\\0&\text{otherwise}\end{cases}

You can expect to win

E[W]=\displaystyle\sum_ww\,P(W=w)=\frac{43\cdot3}{13}-\frac{11\cdot10}{13}=\boxed{\frac{19}{13}}

or about $1.46 per game.

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