probability - 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.

Krishna (last edited 4 years ago) (Expert, Educator @Qalaxia)

Step 1: Perform the given event and note down the all the possible outcomes.

EVENT: Tossing the coin 3 times

Total number of out comes n(A)= {(H, H, H), (H, H, T), (H, T, H), (T, H, H), (H, T, T), (T, H, T), (T, T, H), (T, T, T)} = 2 * 2* 2 = 8

The possible favorable outcomes = Three heads or three tailss = {(H, H, H),(T, T, T)} = 2

Favourable outcomes of Hanif to lose the game n(L) = 8 - 2 = 6

Step 2: Calculate the probability that Hanif will lose the game

P(H) = \frac{n(L)}{n(A)}

= \frac{6}{8}

= \frac{3}{4}