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24 Dec 2009, 05:46
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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.
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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24 Dec 2009, 06:31
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chauhan2011
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?
24 Dec 2009, 06:55
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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
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
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
