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

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

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New post Updated on: 30 Jul 2017, 03:52
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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, 03:33.
Last edited by chetan2u on 30 Jul 2017, 03:52, edited 1 time in total.
Added Topic name and formatted the Q
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Re: When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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New post 30 Jul 2017, 03:35
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
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Re: When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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New post 30 Jul 2017, 03:51
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..
1) prob of getting 1 head+ P of 2 head + P of 3 head + P of 4 head
2) 1-(P of getting 5 head +P of getting 6 heads)

calculation are less in (2)..
solution
P of getting six heads..
\(\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=\frac{1}{2^6}\)
P of getting 5 heads
\(\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=\frac{1}{2^6}*6C5=\frac{6}{2^6}\)..
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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

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New post 30 Jul 2017, 03:56
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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When a fair coin is tossed 6 times, what is the probability that less  [#permalink]

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New post 31 Jul 2017, 20:53
1
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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) \(= 1 - \frac{7}{64} = \frac{64 - 7}{64} = \frac{57}{64}\)

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

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