Question

A game consists of tossing a one-rupee coin three times, and noting its outcome each time. Find the probability of getting

(i) three heads,
(ii) at least two tails.

Answer 1

When a coin is tossed three times, all possible outcomes are
HHH, HHT, HTH, THH, HTT, THT, TTH and TTT.

Number of total outcomes = 8.

(i) Outcome with three heads is HHH.

Number of outcomes with three heads = 1.

∴ P(getting three heads) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{1}{8}$

Thus, the probability of getting three heads is $\frac{1}{8}$.

(ii) Outcomes with atleast two tails are TTH, THT, HTT and TTT.

Number of outcomes with atleast two tails = 4.

∴ P(getting at least two tails) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{4}{8}=\frac{1}{2}$

Thus, the probability of getting at least two tails is $\frac{1}{2}$.