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

We know that when a coin is tossed ‘n’ times.

⇒ Total number of outcome = 2ⁿ

∴ when a coin is tossed 3 times.

⇒ Total number of outcomes = 2³

⇒ Total number of outcomes = 8

⇒ Deskhitha wins if all the tosses give same result i.e. three heads and three tails.

⇒ When 3 coins tossed following cases will appear –

T T T

T T H

T H T

H T T

H H T

H T H

T H H

H H H

⇒ From the above analysis we conclude that there are 1 case where 3 heads and 1 case where three tails are appears.

⇒ And other 6 outcomes are of different results.

⇒ Probability of Deskhitha loose the game –

⇒ P(Deskhitha loose the game) =

⇒ P(Deskhitha loose the game) =

⇒ P(Deskhitha loose the game) =

∴ Probability of Deskhitha loose the game is .