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A fair coin is tossed 5 times.

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A fair coin is tossed 5 times. [#permalink] New post 07 Jul 2017, 12:06
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A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?

A. 2/16
B. 1/4
C. 7/24
D. 5/16
E. 15/32
[Reveal] Spoiler: OA

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Last edited by pranab01 on 26 Jul 2017, 04:37, edited 3 times in total.
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Re: A fair coin is tossed 5 times. [#permalink] New post 26 Jul 2017, 00:24
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Any explanation on the above? Thanks
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Re: A fair coin is tossed 5 times. [#permalink] New post 26 Jul 2017, 04:49
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nancyjose wrote:
Any explanation on the above? Thanks


The total number of outcomes = 2 ^5 =32 (it is because each toss has two possibilities Head or Tail.In general when a coin is tossed n times , the total number of possible outcomes = 2^n)

Let E = event of getting atleast 3 heads .

Atleast means that’s the minimum number of heads and it can be more than that ..ie he can get 3 heads , 4 heads or 5 heads.

So Favorable outcomes E ={3 heads and remaining 2 tails , 4 heads and 1 tail , 5 heads no tail}
={HHHTT,TTHHH,THHHT,HHHHT,THHHH,HTHHH,HHHTH, HHHHH}

So no. of favorable outcomes E =8
So the required probability = 8/32 = ¼
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Intern
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Re: A fair coin is tossed 5 times. [#permalink] New post 26 Jul 2017, 06:32
pranab01 wrote:
nancyjose wrote:
Any explanation on the above? Thanks


The total number of outcomes = 2 ^5 =32 (it is because each toss has two possibilities Head or Tail.In general when a coin is tossed n times , the total number of possible outcomes = 2^n)

Let E = event of getting atleast 3 heads .

Atleast means that’s the minimum number of heads and it can be more than that ..ie he can get 3 heads , 4 heads or 5 heads.

So Favorable outcomes E ={3 heads and remaining 2 tails , 4 heads and 1 tail , 5 heads no tail}
={HHHTT,TTHHH,THHHT,HHHHT,THHHH,HTHHH,HHHTH, HHHHH}

So no. of favorable outcomes E =8
So the required probability = 8/32 = ¼



Thank you this was helpful
Re: A fair coin is tossed 5 times.   [#permalink] 26 Jul 2017, 06:32
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A fair coin is tossed 5 times.

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