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A fair coin is flipped a total of m + n times, where m is greater than n. The probability that there is a run of exactly m consecutive heads is
- (n + 2)/2^(m+1)
- (n + 1)/2^(m+1)
- n/2^(m+1)
- None of these
Correct answer: (n + 2)/2^(m+1)
Solution
The probability of obtaining a run of m consecutive heads when a fair coin is tossed m+n times (m>n) is (n+2)/2^(m+1). Direct enumeration for small m,n (e.g. m=2,n=1 gives 3/8; m=3,n=2 gives 1/4) confirms this formula exactly.
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