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What is the probability of tossing a coin five times and having heads

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Bunuel
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What is the probability of tossing a coin five times and having heads [#permalink] New post   08 Dec 2014, 06:19
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Tough and Tricky questions: Probability.



What is the probability of tossing a coin five times and having heads appear at most three times?

A) 1/16
B) 5/16
C) 2/5
D) 13/16
E) 27/32

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Source: Chili Hot GMAT
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D
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Konstantin1983
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Re: What is the probability of tossing a coin five times and having heads [#permalink] New post   08 Dec 2014, 06:29
I think it is C. Total number of outcomes 25. 3 out 5 is (5!)/(3!2!) = 10. Hence probability is 10/25= 2/5.
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Re: What is the probability of tossing a coin five times and having heads [#permalink] New post   08 Dec 2014, 07:50
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What is the probability of tossing a coin five times and having heads appear at most three times?

A) 1/16
B) 5/16
C) 2/5
D) 13/16
E) 27/32

Total number of outcomes of coin tossed 5 times = \(2^5\) = 32

Number of outcomes with all heads = 1
Number of outcomes with 4 heads =\(C^5_1\)=5

Therefore number of favorable outcome (at most three heads) = 32-(5+1) = 26

Probability (heads appear at most three times) =\(\frac{26}{32} = \frac{13}{16}\)

Answer:D
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Bunuel
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Re: What is the probability of tossing a coin five times and having heads [#permalink] New post   09 Dec 2014, 06:43
Expert Reply
Bunuel wrote:

Tough and Tricky questions: Probability.



What is the probability of tossing a coin five times and having heads appear at most three times?

A) 1/16
B) 5/16
C) 2/5
D) 13/16
E) 27/32

Kudos for a correct solution.

Source: Chili Hot GMAT


The correct answer is D.
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GauravSolanky
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Re: What is the probability of tossing a coin five times and having heads [#permalink] New post   02 Mar 2015, 01:52
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IMO D.
5 heads can come only in one way and for four heads or one tail there is 5 way combinations. So, that tally goes upto 6
Total= 32
Favorable = 32-6=26
Probability= 26/32=13/16

Hope this was helpful ! :)
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Re: What is the probability of tossing a coin five times and having heads [#permalink] New post   02 Mar 2015, 04:17
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Bunuel wrote:

Tough and Tricky questions: Probability.



What is the probability of tossing a coin five times and having heads appear at most three times?

A) 1/16
B) 5/16
C) 2/5
D) 13/16
E) 27/32

Kudos for a correct solution.

Source: Chili Hot GMAT


Total # Outcomes = 2^5 = 32

P(At most 3 heads) = 1-P(atleast 4 heads)

= 1 - (P(4 heads)+P(5 heads))

= 1- (5C4 +5C5)/32

=1 - (5+1)/32

=1 - 6/32

=1-3/16

=13/16

Option D
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Re: What is the probability of tossing a coin five times and having heads [#permalink] New post   25 May 2020, 01:12
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Re: What is the probability of tossing a coin five times and having heads [#permalink]
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