Multiple choice

A normal coin tossed repeatedly until two consecutive heads is obtained. the probability two consecutive heads occurs on the seventh and eight flips is equal to

  1. $\dfrac{11}{256}$
  2. $\dfrac{15}{256}$
  3. $\dfrac{13}{256}$
  4. $\dfrac{17}{256}$
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C Correct answer
Explanation

To get the first HH at flips 7 and 8, the sequence must end in THH. The probability of a specific sequence of length 8 is (1/2)^8 = 1/256. For the sequence to end in THH at position 8, the first 5 flips must not contain HH. The number of such sequences is given by the Fibonacci sequence F(n+2). For n=5, F(7) = 13. Thus, 13/256.