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A card game is played with 52 cards divided equally between four players North, South, East...

A card game is played with 52 cards divided equally between four players North, South, East and West, all arrangements being equally likely. Thirteen of the cards are referred to as trumps. If you know that North and South have ten trumps between them

a. What is the probability that all three remaining trumps are in the same hand?

b. If it is known that the king of trumps is included among the other three, what is the probability that one player has the king and the other the remaining two trumps?

I only need solution to part b. I was able to solve part a. Thanks

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Number of cards each player ( North, South, West, East ) has = 13

And there are 13 cards out of 52 that are referred to as trumps.

Answer b:

  • Case I:

Probability that West has the king trump and East has the remaining two trumps = (1/13) x ( 2/13) = 2/169

  • Case II:

Probability that East has the king trump and West has the remaining two trumps = (1/13) x ( 2/13) = 2/169

Therefore, total probability that one player has the king trump and the other the remaining two trumps = 2/169 + 2/169 = 4/169

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