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

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swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Fri Jul 06, 2018 8:48 am

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

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

The OA is E.

Please, can anyone explain this PS question? I think that the answer would be multiplied by 5 but I'm not sure. I need help. Thanks.

Source: Beat The GMAT — Problem Solving | Fri Jul 06, 2018 8:48 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Fri Jul 06, 2018 9:16 am

The probability of a given pattern of heads or tails in 5 flips is (1/2)^5.

The question asks for probability of getting 4 heads and 1 tail.

Since the 1 tail can occur in any one of the 5 positions, there are 5 patterns of heads and tails.

So 5x(1/2)^5 = [spoiler]E, 5/32[/spoiler]

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by [email protected] » Mon Jul 09, 2018 6:59 am

Hi swerve,

We're told that Rhoda tosses a coin 5 times. We're asked for the probability of getting exactly 4 heads. This question can be approached in a couple of different ways, including as a Permutation.

Since each toss has 2 possible outcomes, with 5 tosses there would be (2)^5 = 32 possible arrangements of results. To flip 4 heads, you would also have to flip 1 tail - and it wouldn't be difficult to 'list out' those possibilities:

HHHHT
HHHTH
HHTHH
HTHHH
THHHH

5 outcomes of the 32 possible will give us 4 heads.

Final Answer: E

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Rich

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Sat Jul 14, 2018 6:20 pm

swerve wrote:Rhoda tosses a coin 5 times. Find the probability of getting 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

Jeffrey Miller
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