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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 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)
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Nov 2012, 14:56, edited 1 time in total.
Renamed the topic and added OA.

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

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New post 02 Nov 2012, 15:03
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clarkkent0610 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 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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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 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) \(( 1/4)^{4}\)

[Reveal] Spoiler:
A

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

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New post 28 Jul 2014, 09:24
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New post 16 Sep 2015, 03:38
Hello from the GMAT Club BumpBot!

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New post 28 Mar 2016, 05:54
AnnaKathpal 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 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) \(( 1/4)^{4}\)

[Reveal] Spoiler:
A


PLEASE SEARCH BEFORE POSTING AND NAME TOPICS PROPERLY: rules-for-posting-please-read-this-before-posting-133935.html
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 30 Oct 2016, 12:25
Hi Bunuel,

I have got a doubt with the usage of Permutation or Combination in such types of questions. For the following problem:http://gmatclub.com/forum/if-jesse-flips-a-coin-seven-times-in-a-row-what-is-the-probability-th-211560.html

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?

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Re: For each player’s turn in a certain board game, a card is   [#permalink] 30 Oct 2016, 12:25
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