• # question_answer 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.

 Set of possible outcomes $=\{HHH,HHT,HTH,THH,HTT,THT,TTH,TTT\}$. (i) Let ${{E}_{1}}$ be the event of getting exactly two heads $\therefore$ Favourable outcomes $=\{HHT,HTH,THH\}$ No. of favourable outcomes $=3$ $P({{E}_{2}})=\frac{3}{8}$ (ii) Let ${{E}_{2}}$ be the event of getting at least two heads. $\therefore$ Favourable outcomes $=\{HHT,HTO,THH,HHH\}$ No. of favourable outcomes $=4$ $P({{E}_{2}})=\frac{4}{8}=\frac{1}{2}$ (iii) Let ${{E}_{3}}$ be the event of getting at least two tails. $\therefore$ Favourable outcomes $=\{HTT,THT,TTH,TTT\}$ $P({{E}_{3}})=\frac{4}{8}=\frac{1}{2}$

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