A coin is tossed until it falls headstailsheads in that orde

A coin is tossed until it falls heads-tails-heads, in that order, on three consecutive tosses. Find the expected number of tosses necessary.

Solution

The coin has been tossed 3 times. We are going to toss untill first success, here success means getting \"heads-tails-heads\". This is case of geometric distribution, we are estimating \"trials\" requires before sucess.

x - number of trials required before bfore 1st sucess.

x follows geometric distribution with probability (p)

To find \"p\",

Probability of getting head-tail-head, it will occor once whithin all sample space.

Sample space = {HHH,HHT,HTH,THH,TTH,THT,HTT,TTT} - these are all possible outcomes.

n(s) = 8

p = 1/8 as we have just one value fromm 8 of them.

Now for geometric distribution, mean = 1/p

=1/(1/8)

=8

Hence we may claim that expected trails required for getting Head-tail-Head is 8.