question_answer

Three distinct coins are tossed together. Find the probability of getting

(i) at least 2 heads

(ii) at most 2 heads

Answer:

Total number of possible outcomes \[=8\]

(i) Let \[{{E}_{1}}\] be the event of getting at least two heads Favourable outcomes = (H, H, T), (T, H, H), (H, T, H), (H, H, H)

Number of favourable outcomes \[=4\]

P (getting at least two heads) \[=P({{E}_{1}})=\frac{4}{8}=\frac{1}{2}\]

(ii) Let \[{{E}_{2}}\] be the event of getting at most two heads. Favourable outcomes = (H, T, T), (T, H, T), (T, T, H), (H, H, T), (H, T, H), (T, H, H), (T, T, T)

Number of favourable outcomes \[=7\]

P (getting at most two heads) \[=P({{E}_{2}})=\frac{7}{8}\]