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STATS Example 4 (Bridge)

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Question;Example 4 (Bridge): In the card game bridge 52 cards are dealt with equal chance for all sets of hands of 13 each to East, West, North and South. Given that North and South have a total of 8 spades, what is the chance that East has 3 of the remaining 5 spades?the answer is given in the problem (example 4) but i still do not understand the E, Fi, F and why P(F1) = P(F2) = P(F3) = P(F)/M (check out the attached file)i can understand that there remains totally 26 cards to choose 13, 3 out of 5 spades, and then 10 out of 21 other cards. then the equation from this condition is (5 choose 3)*(21 choose 10) / (26 choose 13) = 0.339.however, why not take the north and south possible cards combination into account, which will result in a smaller probability that E has 3 out of 5 spades. different cards combo in north and south hands will result in different cards combo in east, right? but i do not know how?

 

Paper#61688 | Written in 18-Jul-2015

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