Question

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

A = At most two tails, B = At least one tail.

Answer 1

Consider the given events.
A = At most two tails
B = At least one tail

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

\[\text{ Now } , \]
\[A \cap B = {(T, T, H), (T, H, H), (H, H, T), (T, H, T), (H, H, T), (H, T, T)} \]

\[\therefore \text{ Required probability }  = P\left( A/B \right) = \frac{n\left( A \cap B \right)}{n\left( B \right)} = \frac{6}{7}\]