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if you draw two clubs on consecutive draws with replacement from a standard deck of cards you $9 .Otherwise you will pay me $4. Question:Find the expected value of the proposition round your answer to two decimal places. Losses must be expressed as negative values .Answer: $_____

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EXPLANATION

If we draw two clubs on consecutive draws with replacement from a standard deck with 52 cards and 13 clubs, we can apply the following relationship:

The probability that both cards are clubs is as follows:

[tex]\frac{13}{52}\cdot\frac{13}{52}=\frac{1}{16}=0.0625[/tex]

If both cards are clubs, we will receive $9, therefore:

0.0625 * (9) = 0.5625

If both cards are not clubs, we will pay $4:

1 - 0.0625 = 0.9375

Now, in this case we will need to pay:

0.9375 * (4) = -3.75

Hence, the Expected Value of the bet is:

0.5625 - 3.75 = -3.19

In conclusion, the Expected Value is $ -3.19

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