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

exactly two heads

#### Solution

\[\text{ When 3 coins are tossed together, the outcomes are as follow }: \]

\[S = \left\{ \left( h, h, h \right), \left( h, h, t \right), \left( h, t, h \right), \left( h, t, t \right), \left( t, h, h \right), \left( t, h, t \right), \left( t, t, h \right), \left( t, t, t \right) \right\}\]

\[\text{ Therefore, the total number of outcomes is 8 }. \]

\[\text{ Let A be the event of getting triplets having exactly 2 heads } . \]

\[\text{ Triplets having exactly 2 heads }: \left( h, h, t \right), \left( h, t, h \right), \left( t, h, h \right)\]

\[\text{ Therefore, the total number of favourable outcomes is 3 }. \]

\[P\left( A \right) = \frac{\text{ Number of favourable outcomes }}{\text{ Total number of outcomes }} = \frac{3}{8}\]