Question

Two coins are tossed once. Find P (A/B) in each of the following:
(i) A = Tail appears on one coin, B = One coin shows head.
(ii) A = No tail appears, B = No head appears.

Answer 1

(i) Consider the given events.
A = Tail appears on one coin
B = One coin shows head

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

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

(ii) Consider the given events.
A = No tail appears
B = No head appears

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

$$\begin{gathered} \mathrm{Now}, \\ A\cap B=\left\{\varphi \right\} \\ \therefore \mathrm{Required}\mathrm{probability}=P\left(A/B\right)=\frac{n\left(A\cap B\right)}{n\left(B\right)}=\frac{0}{1}=0 \end{gathered}$$