Question

A coin is tossed three times. Find P (A/B) in each of the following:

A = At least two heads, B = At most two heads

Answer 1

Consider the given events.
A = At least two heads
B = At most two heads

Clearly,
A = {(H, H, H), (H, T, H), (T, H, H), (H, H, T)}
B = {(T, T, T), (H, T, H), (T, H, H), (H, H, T), (T, H, T), (H, H, T), (H, T, T)}

\[\text { Now } , \]
\[A \cap B = \left\{ \left( H, T, H \right), \left( T, H, H \right), \left( H, H, T \right) \right\}\]
\[ \therefore \text{ Required probability }  = P\left( A/B \right) = \frac{n\left( A \cap B \right)}{n\left( B \right)} = \frac{3}{7}\]