Question

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

at least one head and one tail

Answer 1

\[\text{ When 3 coins are tossed together, the outcomes are as follows } \]
\[S = \left\{ \left( h, h, h \right), \left( h, h, t \right), \left( h, t, h \right), \left( h, t, t \right), \left( t, h, h \right), \left( t, h, t \right), \left( t, t, h \right), \left( t, t, t \right) \right\}\]
\[\text{ Therefore, the total number of outcomes is 8 } . \]

\[\text{ Let A be the event of getting triplets having at least one head and one tail } . \]
\[\text{ Triplets having at least one head and one tail }: \left( h, h, t \right), \left( h, t, h \right), \left( t, h, h \right), \left( h, h, t \right), \left( t, t, h \right), \left( t, h, t \right)\]
\[\text{ Therefore, the total number of favourable outcomes is 6 } . \]
\[P\left( A \right) = \frac{\text{ Number of favourable outcomes }}{\text{ Total number of outcomes }} = \frac{6}{8} = \frac{3}{4}\]