Question

A fair coin is continually flipped until heads appears for the 10th time. Let X denote the number of tails that occur. Compute the probability mass function of X.

Answer 1

Answer:

P(X=n) = [n+9 C 9] (0.5)ⁿ⁺¹⁰

Explanation:

Number of times a head appears = 10

Total number of times the coin is flipped = X + 10

X = number of tails

Since it is certain that the last flip is a head , probability mass function of tail can be gotten out of (X + 10 -1) flips = X + 9 flips

P(X=n) = [n+9 C 9] (0.5)ⁿ⁺¹⁰