Question

A fair coin is tossed until a head or five tails occur. If X denotes the number of tosses of the coin, find the mean of X.

Answer 1

Given X denotes the number of coins. 

Coins is tossed until a head or five tails accur therefore, it is clear if on X = 1, head comes then the process will be stopped and if tail comes then coin will be tossed second time. 

Clearly it will be repeated again and again till 5 tails come maximum. 

Then the value of X will be 1,2, 3,4, 5 

S = {H, TH, TTH, TTTH or TTTTH, TTTTT} 

∴ Probability that head comes in first throw

P(X = 1) = 1/2

Similarly

Hence, Probability distribution will be like this