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.

Answer:

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 \[=\{HTT,THT,TTH,TTT\}\]

\[P({{E}_{3}})=\frac{4}{8}=\frac{1}{2}\]