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

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Current Student
Joined: 09 May 2017
Posts: 15
WE: Information Technology (Consulting)
When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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Updated on: 30 Jul 2017, 04:52
13
00:00

Difficulty:

45% (medium)

Question Stats:

66% (02:09) correct 34% (02:15) wrong based on 108 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

Originally posted by 3newton on 30 Jul 2017, 04:33.
Last edited by chetan2u on 30 Jul 2017, 04:52, edited 1 time in total.
Added Topic name and formatted the Q
Current Student
Joined: 09 May 2017
Posts: 15
WE: Information Technology (Consulting)
Re: When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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30 Jul 2017, 04:35
Cant it be done this way?

ways of getting less than 5 heads -

1 or 2 or 3 or 4

Total no of possible outcomes - 2^6 = 64

therefore final probability =

1/64 + 2/64 + 3/64 + 4/64
Math Expert
Joined: 02 Aug 2009
Posts: 7763
Re: When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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30 Jul 2017, 04:51
1
2
3newton 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

Hi,

two ways to do it..

calculation are less in (2)..
solution
$$\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=\frac{1}{2^6}$$
$$\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=\frac{1}{2^6}*6C5=\frac{6}{2^6}$$..
Multiplication by 6C5 is to choose 5 times out of 6 when it is H... example HHHHHT, HHHHTH.......
so answer = $$1-\frac{1}{2^6}-\frac{1}{2^6}=1-\frac{7}{64}=57/64$$
E
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Current Student
Joined: 09 May 2017
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WE: Information Technology (Consulting)
Re: When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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30 Jul 2017, 04:56
so my approach follows your 1st, but i will get a different answer !

Can you please explain your 1st and also tell me whats wrong with mine?
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Concentration: Technology, Strategy
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When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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31 Jul 2017, 21:53
1
3
3newton 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

Can be solved by Compliment $$=>$$ P (event happens) $$= 1 -$$ P (event Does not happen)

P (Less than $$5$$ heads) $$= 1-$$[P ($$5$$ heads) + P ($$6$$ heads)]

P ($$5$$ heads) $$= \frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}* \frac{1}{2} = (\frac{1}{2}) ^ 6 * 6C5 = \frac{1}{64} * \frac{6 * 5!}{5!} = \frac{1}{64} * 6 = \frac{6}{64}$$

P ($$6$$ heads) $$= \frac{1}{2} *\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}* \frac{1}{2} = (\frac{1}{2}) ^ 6 = \frac{1}{64}$$

P (Less than $$5$$ heads) $$= 1- (\frac{6}{64} + \frac{1}{64})$$

P (Less than $$5$$ heads) $$= 1- (\frac{6 + 1}{64}) = 1 - (\frac{7}{64})$$

P (Less than $$5$$ heads) $$= 1 - \frac{7}{64} = \frac{64 - 7}{64} = \frac{57}{64}$$

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Re: When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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09 Aug 2018, 09:04
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Re: When a fair coin is tossed 6 times, what is the probability that less   [#permalink] 09 Aug 2018, 09:04
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