Question

Die A has $4$ red and $2$ white faces where as die $B$ has two red and $4$ white faces. $A$ fair coin is tossed. If head turns up, the game continues by throwing die A, if tail turns up then die B is to be used. Probability of getting a red face at any throw is

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. none of these

Answer 1

The correct option is A $\frac{1}{2}$

We can get a red face if (i) Head and Red from A or (ii) Tail and Red from B
Probability of getting a red face = $\frac{1}{2}\ast \frac{4}{6}+\frac{1}{2}\ast \frac{2}{6}=\frac{6}{12}=\frac{1}{2}$