Question

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Answer 1

If `H` represents a Head and `T` represents Tail, then, Hanif will win if outcomes are `(H,H,H)` or `(T,T,T)` .
So, `E_w = 2`
Total number of possible outcomes, `n(S) = 3^2 = 9`
So,Probability Hanif will win ,`P(E_w) = E_w/(n(S)) = 2/9`
Probability Hanif will lose `=1-P(E_w) = 1-2/9 =7/9`