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Rhoda tosses a coin 5 times. Find the probability of getting exactly 4

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Rhoda tosses a coin 5 times. Find the probability of getting exactly 4  [#permalink]

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New post Updated on: 24 Aug 2017, 23:58
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Rhoda tosses a coin 5 times. Find the probability of getting exactly 4 heads.

A. 1/32
B. 1/16
C. 3/32
D. 1/8
E. 5/32


Answer: 5/32


I fail to understand why have we multiplied by (5).

Originally posted by ruchi857 on 17 May 2016, 04:21.
Last edited by Bunuel on 24 Aug 2017, 23:58, edited 2 times in total.
Edited the question.
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Re: Rhoda tosses a coin 5 times. Find the probability of getting exactly 4  [#permalink]

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New post 17 May 2016, 04:30
ruchi857 wrote:
Rhoda tosses a coin 5 times. Find the probability of getting exactly 4 heads.

Answer: 5/32


I fail to understand why have we multiplied by (5).


You can have the following 5 cases:
THHHH
HTHHH
HHTHH
HHHTH
HHHHT

Each of the 5 cases has the probability of (1/2)^5, thus the overall probability is 5*(1/2)^5.
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Re: Rhoda tosses a coin 5 times. Find the probability of getting exactly 4  [#permalink]

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New post 21 May 2016, 10:54
Would be glad if I get a more elaborate explanation to this problem.
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Re: Rhoda tosses a coin 5 times. Find the probability of getting exactly 4  [#permalink]

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New post 10 Jul 2016, 05:59
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Please note that the coin problems are very similar to alphabet problems and can be solved in the same way.

Exactly 4 heads out of 5 would be: HHHHT, HHTHH, or many other combinations.

therefore, no. of possible combinations are 5!/4!*1! = 5

Probability = 5/2^5 = 5/32
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Re: Rhoda tosses a coin 5 times. Find the probability of getting exactly 4  [#permalink]

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New post 08 Dec 2016, 00:39
To get 4 heads from 5 tosses there must be 4H and 1T. The probability of getting 4H and then 1T is 1/(2^5).
However, there are 5 ways to arrange 4H and 1T in 5 tosses. This is found using combinations nCr: 5!/(4!)(1!).
Multiplying the probability by the number of arrangements = 5/32.
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Re: Rhoda tosses a coin 5 times. Find the probability of getting exactly 4  [#permalink]

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New post 14 Jul 2018, 19:27
ruchi857 wrote:
Rhoda tosses a coin 5 times. Find the probability of getting exactly 4 heads.

A. 1/32
B. 1/16
C. 3/32
D. 1/8
E. 5/32


The probability of H-H-H-H-T in this order is (½)^4 (½) = 1/32. However, the 4 heads and 1 tail can be arranged in 5!/4! = 5 ways. Therefore, the probability of getting 4 heads and 1 tail is 5 x 1/32 = 5/32.

Answer: E
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Re: Rhoda tosses a coin 5 times. Find the probability of getting exactly 4 &nbs [#permalink] 14 Jul 2018, 19:27
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