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A fair coin is tossed 5 times. What is the probability that

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Senior Manager
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A fair coin is tossed 5 times. What is the probability that [#permalink] New post 24 May 2006, 22:30
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A fair coin is tossed 5 times. What is the probability that it lands heads up at least twice?

A. 1/16
B. 5/16
C. 2/5
D. 13/16
E. 27/32
[Reveal] Spoiler: OA
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Re: A fair coin is tossed 5 times. What is the probability that [#permalink] New post 24 May 2006, 22:44
5/16

Two heads can be in a toss of 5 times in 5C2 = 10 ways

Each way(number of times at least two heads will come) has a probability of 1/32.

Hence 10*1/32 = 5/16
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Re: A fair coin is tossed 5 times. What is the probability that [#permalink] New post 24 May 2006, 22:45
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It is B....

Total possible outcomes=2*2*2*2*2=32
Favourable outcomes=5C2=10

Probability=10/32=5/16....
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Re: A fair coin is tossed 5 times. What is the probability that [#permalink] New post 24 May 2006, 22:52
SimaQ wrote:
It is B....

Total possible outcomes=2*2*2*2*2=32
Favourable outcomes=5C2=10

Probability=10/32=5/16....


going by your logic - the favourable outcomes should be 5C2 + 5C3 +5C4 + 5C5 ( question says at least 2..right?)
= 10 + 10 + 5 + 1 =26

hence prob = 26/32 = 13/16
ie choice D
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Re: A fair coin is tossed 5 times. What is the probability that [#permalink] New post 24 May 2006, 23:02
iced_tea wrote:
SimaQ wrote:
It is B....

Total possible outcomes=2*2*2*2*2=32
Favourable outcomes=5C2=10

Probability=10/32=5/16....


going by your logic - the favourable outcomes should be 5C2 + 5C3 +5C4 + 5C5 ( question says at least 2..right?)
= 10 + 10 + 5 + 1 =26

hence prob = 26/32 = 13/16
ie choice D


Yes.......
Calculated ofr only two heads.....

Favorable outcomes are 5C2+5C3 + 5C4+5C5
=> 10+10+5+1
=> 26
26/32 = 13/16

Hence D
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Re: A fair coin is tossed 5 times. What is the probability that [#permalink] New post 24 May 2006, 23:45
Yep my bad..... missed the at least part.... must be more concentrated.
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Re: A fair coin is tossed 5 times. What is the probability that [#permalink] New post 25 May 2006, 12:17
I don't understand whu you sum up "10+10+5+1".

Can someone explain it?
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Re: A fair coin is tossed 5 times. What is the probability that [#permalink] New post 25 May 2006, 22:31
netcaesar wrote:
I don't understand whu you sum up "10+10+5+1".

Can someone explain it?


We sum up the number of ways you can toss heads up 2 times, 3 times, 4 times and 5 times....
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Re: A fair coin is tossed 5 times. What is the probability that [#permalink] New post 06 Aug 2014, 19:43
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Probability of all tails = 1/32
Probability of 4 tails = 5/32
------------------------------------------------------------------------------
Probability of all tails or 4 tails = 1/32 + 5/32 = 6/32 = (3/16)
------------------------------------------------------------------------------

Therefore probability of at least 2 heads = 1- Prob of all or 4 tails = 1- (3/16) = 13/16

Hence (D)
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Re: A fair coin is tossed 5 times. What is the probability that [#permalink] New post 07 Aug 2014, 09:22
Fair coin is tossed 5 times . Hence total number of outcomes = 2^5 = 32.

Problem asks for probability of getting atleast heads twice. Hence if we calculate probability of getting Heads exactly once and probability of not getting Heads at all and subract it from the total probability of the event which is 1 (As total probability of certain event will be always 1) we can get the probability of getting atleast heads twice.

Probability of getting exactly one head and no heads= (Number of possible outcomes [ HTTTT , THTTT, TTHTT, TTTHT, TTTTH , TTTTT] = 6)/ (Total possible outcomes = 32)

=> 6/32 = 3/16

Hence probability of getting atleast heads twice = 1 - (3/16) = 13/16 => Choice [D]
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Re: A fair coin is tossed 5 times. What is the probability that [#permalink] New post 17 Sep 2014, 06:14
netcaesar wrote:
A fair coin is tossed 5 times. What is the probability that it lands heads up at least twice?

A. 1/16
B. 5/16
C. 2/5
D. 13/16
E. 27/32


Sol:

2H3T, 3H2T, 4H1T, 5H calculating this will take longer than calculating 5T, 4T1H

lets calculate 5T, 4T1H

5T= 1/2^5 = 1/32
4T1H = (1/32) (5!/4!) = 5/32

5T+4T1H= 6/32 = 3/16

1- (5T+4T1H) = 1-3/16 = 13/16

(D)
Re: A fair coin is tossed 5 times. What is the probability that   [#permalink] 17 Sep 2014, 06:14
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