A coin is tossed until a head appears or tail appears 4 times in succession Match P.D. of x.

Match List-I with List-II. (x is number of times the coin is tossed)

Choose the correct answer from the options given below :

(A)-(II), (B-(I), (C)-(III), (D)-(IV)

The correct answer is Option (2) → (A)-(II), (B-(I), (C)-(III), (D)-(IV)

$P(X=1)=P(H)=\frac{1}{2}$

$P(X=2)=P(T)×P(H)=\frac{1}{2}×\frac{1}{2}=\frac{1}{4}$

$P(X=3)=P(T)×P(T)×P(H)=\frac{1}{2}×\frac{1}{2}×\frac{1}{2}=\frac{1}{8}$

$P(X=4)=P(T)×P(T)×P(T)×(P(T)×P(H))=\frac{1}{2}×\frac{1}{2}×\frac{1}{2}×(\frac{1}{2}×\frac{1}{2})=\frac{1}{8}$