Question
Asked Nov 6, 2019
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Nancy and Karen play a game of cards as follows. Nancy draws 3 cards out of a regular deck of 52 cards without replacement: if she draws at least one ace, she wins. Otherwise, Karen wins. Suppose they play the games 10 times, and after each time, the cards are placed back in the deck and reshuffled.

(a) Find the probability that Nancy wins exactly 4 times.

(b) Find the expected number of times Karen wins.

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Expert Answer

Step 1

From the given information,

Total cards = 52.

Number of aces = 4,

Number of draws (without replacement) = 3

Step 2

a)

It is required to calculate that Nancy wins exactly four times.

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P(She drwas at least on ace ) = 1- P(no ace) 48 47 46 =1-_> 52 51 50 0.21

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Step 3

The probability that Nancy wins e...

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10 P(wins 4) (0.21) (1-0.21) =0.09

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