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# For each player's turn in a certain board game, a card is

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For each player's turn in a certain board game, a card is [#permalink]  06 May 2012, 10:29
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For each player's turn in a certain board game, a card is drawn. 3/4 of the cards in the deck are marked with a circle, and the 1/4 remaining cards are marked with a square. If five players draw a card and then return it to the deck, what is the probability that at least four of the cards drawn are marked with a square?

A. (1/4)^3
B. 5(1/4)^3
C. 3/4(1/4)^4
D. 2/3(1/4)^4
E. (1/4)^5
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Re: For each player's turn in a certain board game, a card is [#permalink]  06 May 2012, 10:41
Galiya wrote:
For each player's turn in a certain board game, a card is drawn. 3/4 of the cards in the deck are marked with a circle, and the 1/4 remaining cards are marked with a square. If five players draw a card and then return it to the deck, what is the probability that at least four of the cards drawn are marked with a square?

A. (1/4)^3
B. 5(1/4)^3
C. 3/4(1/4)^4
D. 2/3(1/4)^4
E. (1/4)^5

At least four of the cards drawn are marked with a square means 4 or all 5 cards are marked with a square.

P=P(SSSC)+P(SSSSS)=\frac{5!}{4!}*(\frac{1}{4})^4*\frac{3}{4}+(\frac{1}{4})^5=\frac{1}{4^3}, we are multiplying first case by \frac{5!}{4!}, since SSSSC can occur in several ways: SSSSC, SSSCS, SSCSS, ... Notice that the number of occurrences of SSSSC basically is the number of arrangements of 5 letters SSSSC out of which 4 S's are identical, so it's \frac{5!}{4!}.

Hope it's clear.
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Re: For each player's turn in a certain board game, a card is [#permalink]  06 May 2012, 10:56
great!Thank you so much,Bunuel!
Re: For each player's turn in a certain board game, a card is   [#permalink] 06 May 2012, 10:56
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