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

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Manager
Joined: 15 Jan 2011
Posts: 88
For each player's turn in a certain board game, a card is  [#permalink]

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06 May 2012, 09:29
1
14
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Difficulty:

65% (hard)

Question Stats:

63% (02:28) correct 37% (02:47) wrong based on 178 sessions

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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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Joined: 02 Sep 2009
Posts: 62691
Re: For each player's turn in a certain board game, a card is  [#permalink]

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06 May 2012, 09:41
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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.

$$P=P(SSSSC)+P(SSSSS)=\frac{5!}{4!}*(\frac{1}{4})^4*\frac{3}{4}+(\frac{1}{4})^5=\frac{1}{4^3}$$, 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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Manager
Joined: 15 Jan 2011
Posts: 88
Re: For each player's turn in a certain board game, a card is  [#permalink]

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06 May 2012, 09:56
great!Thank you so much,Bunuel!
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Re: For each player's turn in a certain board game, a card is  [#permalink]

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22 Dec 2019, 00:24
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Re: For each player's turn in a certain board game, a card is   [#permalink] 22 Dec 2019, 00:24
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