Question

A coin is tossed three times, if head occurs on first two tosses, find the probability of getting head on third toss.

Answer 1

Consider the given events.
A = Getting head on third toss
B = Getting head on first two tosses

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

$$\begin{gathered} \mathrm{Now}, \\ A\cap B=\left\{H,H,H\right\} \\ \therefore \mathrm{Required}\mathrm{probability}=P\left(A/B\right)=\frac{n\left(A\cap B\right)}{n\left(B\right)}=\frac{1}{2} \end{gathered}$$