Question

Three different coins are tossed together. Find the probability of getting
(i) exactly two heads
(ii) at least two heads
(iii) at least two tails

Answer 1

When we toss three coins simultaneously then the possible of outcomes are:

$HHH$ or $HHT$ or $HTH$ or $THH$ or $HTT$ or $THT$ or $TTH$ or $TTT$ respectively;

Where $H$ is denoted for head and $T$ is denoted for tail.

Therefore, total numbers of outcome are $2^3=8$

(i) Exactly two heads

Favourable cases $=\{HHT,HTH,THH\}$

Probability of getting exactly two heads $=\frac{3}{8}$

(ii) At least two heads

Favourable cases $=\{HHH,HHT,HTH,THH\}$

Probability of getting at least two heads $=\frac{4}{8}=\frac{1}{2}$

(iii) At least two tails

Favourable cases $=\{HTT,THT,TTH,TTT\}$

Probability of getting at least two tails $=\frac{4}{8}=\frac{1}{2}$