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For each players turn in a certain board game, a card is [#permalink]

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02 Nov 2012, 13:43

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For each players 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 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. 1/4^4 C. 5*(1/4^3) D. 1/4^5 E. (3/2)*(1/4^4)

For each players 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 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. 1/4^4 C. 5*(1/4^3) D. 1/4^5 E. (3/2)*(1/4^4)

The probability of circle is 3/4 and the probability of square is 1-3/4=1/4.

We want the probability that out of 5 cards drawn 4 OR 5 are squares.

The probability of 4 squares or the probability of SSSSC, is \(P(SSSSC)=\frac{5!}{4!}*(\frac{1}{4})^4*(\frac{3}{4})=\frac{15}{4^5}\). We are multiplying by \(\frac{5!}{4!}=5\) since SSSSC scenario can occur in 5 ways: SSSSC, SSSCS, SSCSS, SCSSS, and CSSSS (number of premutations of 5 letters SSSSC out of which 4 S's are identcal);

The probability of 5 squares or the probability of SSSSS, is simply \(P(SSSSS)=(\frac{1}{4})^5\).

Therefore the overall probability is \(\frac{15}{4^5}+\frac{1}{4^5}=\frac{1}{4^3}\).

Answer: A.

P.S. Please indicate OA for PS problems.
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Re: For each players turn in a certain board game, a card is [#permalink]

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28 Jul 2014, 08:24

Hello from the GMAT Club BumpBot!

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Re: For each players turn in a certain board game, a card is [#permalink]

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16 Sep 2015, 02:38

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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For each players 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 remaining cards are marked with a square. If 5 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) \(3/2( 1/4 )^{4}\) (E) \(( 1/4)^{4}\)

For each players 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 remaining cards are marked with a square. If 5 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) \(3/2( 1/4 )^{4}\) (E) \(( 1/4)^{4}\)

In the above problem bernoulli's theoreom is used: 7C5(There are 7C5 ways that the heads can be placed in 7 times) but in this problem permutation is used: (number of premutations of 5 letters SSSSC out of which 4 S's are identical).

Are the usage of these both interchangeable? Do they mean the same? If yes, can you please explain me how?

gmatclubot

Re: For each players turn in a certain board game, a card is
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30 Oct 2016, 11:25

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