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# When a fair coin is tossed 6 times, what is the probability that less

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Math Expert
Joined: 02 Sep 2009
Posts: 60625
When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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15 Nov 2019, 01:23
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Difficulty:

55% (hard)

Question Stats:

62% (01:55) correct 38% (02:27) wrong based on 65 sessions

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When a fair coin is tossed 6 times, what is the probability that less than 5 heads are tossed?

A. 7/64
B. 5/16
C. 2/3
D. 49/64
E. 57/64

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Joined: 29 Jun 2019
Posts: 470
Re: When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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15 Nov 2019, 08:49
1- (6C6×1/2^6 + 6C5×1/2^5 ×1/2)= 1-(1/64 +6/64)=57/64

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Joined: 16 Aug 2019
Posts: 11
Location: India
Concentration: Human Resources, Real Estate
GPA: 3.3
Re: When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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16 Nov 2019, 01:14
count the prob of getting all head and 5 heads out of 6,

use combination 6C6 + 6C5 = 7,
total outcomes= 2^6= 64
favorable 64-7= 57
P=57/64
Manager
Joined: 10 Dec 2017
Posts: 176
Location: India
Re: When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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16 Nov 2019, 01:21
Bunuel wrote:
When a fair coin is tossed 6 times, what is the probability that less than 5 heads are tossed?

A. 7/64
B. 5/16
C. 2/3
D. 49/64
E. 57/64

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5H 1T( !6/!5*!1) or 6H(!6/!6)
Total cases= 6+1=7
P(not required)=7/64
P(required)=1-7/64
=57/64
E:)
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Concentration: Sustainability, Marketing
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Re: When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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16 Nov 2019, 03:48
P of atleast 5tails = 6c6*(1/2)^6 + 6c5*(1/2)^6 ; (1/64+6/64) ; 7/64
P of Heads<5 ; 1-7/64 ; 57/64
IMO E

Bunuel wrote:
When a fair coin is tossed 6 times, what is the probability that less than 5 heads are tossed?

A. 7/64
B. 5/16
C. 2/3
D. 49/64
E. 57/64

Are You Up For the Challenge: 700 Level Questions
Re: When a fair coin is tossed 6 times, what is the probability that less   [#permalink] 16 Nov 2019, 03:48
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