Question

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

Answer 1

S denotes Sample space of the given condition
`S={H,TH, TTH, TTTH, TTTTH, TTTTTTTTT}` `X=1,2,3,4,5`
`P(X=1)=P(H)=1/2`
`P(X=2)=P(TH)=P(T)*P(H)=1/4`
`P(X=3)=P(TTH)=1/(2^3)=1/8`
`P(X=4)=P(TTTH)=1/(2^4)=1/16`
`P(X=5)=P(TTTH,TTTTT)=1/(2^5)+1/(2^5)=1/16`
`E(X)=SigmaxP(X=x)=1*1/2+2*1/4+3*1/8+4*1/16+5*1/16`
`=(8+8+6+4+5)/16`
`=31/16=1.90`
Therefore, Mean`=1.9`