Maths 高手請答

2007-11-19 6:57 am

1.Paula and Mary take turns drawing a card at random from a suit of 13 cards,
and Paula draws first.
The first to draw the ace is the winner.Find the probability that Paula will win id ,after each drawing ,the card is replaced.

Ans:13/25

plz 列steps!

回答 (1)

用戶195274

2007-11-19 7:22 am

✔ 最佳答案

P(Paula wins)
= P(Paula draws ace in the first round) + P(Both Paula and Mary do not draw ace in the first round and Paula draws ace in the second round) + P(Both Paula and Mary do not draw ace in the first round and second round and Paula draws ace in the third round) + ...
= 1/13 + (12/13)(12/13)(1/13) + (12/13)(12/13)(12/13)(12/13)(1/13) + ...
= 1/13 + (144/169)(1/13) + (144/169)^2(1/13) + ..., which is the sum of a infinite geometric sequence with common ratio 144/169
= (1/13)/[1- (144/169)]
= (1/13)/(25/169)
=13/25

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