If you draw two diamonds on two consecutive draws without replacement from a sta

Question

If you draw two diamonds on two consecutive draws without replacement from a standard deck of cards you win $179. Otherwise you pay me $10.
Find the expected value of the proposition. Round your answer to two decimal places. Looses must be expressed as negative values. If you draw two diamonds on two consecutive draws without replacement from a standard deck of cards you win $179. Otherwise you pay me $10.
Find the expected value of the proposition. Round your answer to two decimal places. Looses must be expressed as negative values.
Find the expected value of the proposition. Round your answer to two decimal places. Looses must be expressed as negative values.

Explanation / Answer

The probability of drawing 1 diamond out of 13 diamonds from a deck of cards is 13/52. The probability of drawing another diamond out of 12 diamonds from 51 cards is 12/51.

Therefore, probability of drawing two diamonds in consecutive draws is: 13/52*12/51=0.0588.

The expected values, E[X]=0.0588*179+(1-0.0588)*(-10)=$1.11

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