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# A fair coin is tossed 10 times. What is the probability that

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A fair coin is tossed 10 times. What is the probability that [#permalink]  24 Dec 2009, 04:46
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A fair coin is tossed 10 times. What is the probability that two heads do not occur consecutively?

A) 1/ 2^4
B) 1/2^3

C)1/2^5

D) None of the above

Bunuel ,

Could yo help with this one please.
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Re: A fair coin is tossed 10 times [#permalink]  24 Dec 2009, 05:31
Expert's post
chauhan2011 wrote:
Bunuel ,

Could yo help with this one please.

A fair coin is tossed 10 times. What is the probability that two heads do not occur consecutively?

A) 1/ 2^4

B) 1/2^3

C)1/2^5

D) None of the above

This is very hard problem, way beyond the GMAT scope. It was discussed before and many solutions have been given. Here is mine:

Possible number of patterns (total number of combinations) 2^n (each time either H or T=2 outcomes, 10 times=2^10).

Let's check two consecutive H:
If we toss once we'll have 2^1=2 combinations: H, T - 2 outcomes with NO 2 consecutive H.
If we toss twice we'll have 2^2=4 combinations: HT, TH, TT, HH - 3 outcomes with NO 2 consecutive H.
If we toss 3 times we'll have 2^3=8 combinations: TTT, TTH, THT, HTT, HTH, HHT, THH, HHH 5 outcomes with NO 2 consecutive H.
If we toss 4 times we'll have 2^4=16 combinations:... 8 outcomes with NO 2 consecutive H.
...

On this stage we can see the pattern in "no consecutive H": 2, 3, 5, 8...

I guess it's Fibonacci type of sequence and it will continue: 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

144 is outcomes with no consecutive H if we toss 10 times.

P(no two consecutive H in 10 toss)=144/2^10=144/1024=14.0625%

Other solutions and discussion at: probability-coin-toss-57447.html

Hope it helps. BTW were did you find this question?
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Re: A fair coin is tossed 10 times [#permalink]  24 Dec 2009, 05:55
Thanks Bunuel ,

Though i saw so many explainations but didnt get them well.
yours is very undertandable and i guess this will not be in the scope of GMAT.

I found this on the link below at GMAT club

gmatclub.com/forum/combined-probability-question-87294.html
Re: A fair coin is tossed 10 times   [#permalink] 24 Dec 2009, 05:55
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