# 23.   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.

H Harsh Kankaria

The possible outcomes when a coin is tossed 3 times: (Same as 3 coins tossed at once!)

{HHH, HHT, HTH, HTT, THH, TTH, THT, TTT}

Number of total possible outcomes = 8

For Hanif to win, there are only two favourable outcomes: {HHH, TTT}

Number of favourable outcomes = 2

$\therefore P(Hanif\ will\ win) = \frac{favourable\ outcomes}{total\ outcomes} = \frac{2}{8}$

$= \frac{1}{4}$

$\therefore P(Hanif\ will\ lose) = 1-\frac{1}{4}$

$=\frac{3}{4}$

Therefore, the probability that Hanif will lose is $\frac{3}{4}$

Exams
Articles
Questions