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

The correct answer is $frac{3}{4}$

As the coin is tossed 3 times, all the possibles outcomes can be listed down as below.



As can be seen from above, David will win if he gets head, head and head or tail, tail and tail in successive tossings.
There are 2 possible outcomes i.e. 1st and 8th only in the above table where David can win.
∴Probability of David winning the game = P(E) = $\frac{2}{8}$ = $\frac{1}{4}$

∴Probability of David not winning the game = P(Ē) = 1 - P(E) = 1 - $\frac{1}{4}$ = $\frac{3}{4}$