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)
| List-I | List-II | ||
| (A) | 1 | (I) | $\frac{1}{4}$ |
| (B) | 2 | (II) | $\frac{1}{2}$ |
| (C) | 3 | (III) | $\frac{1}{8}$ |
| (D) | 4 | (IV) | $\frac{1}{8}$ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(II), (B-(I), (C)-(III), (D)-(IV)
$P(X=1)=P(H)=\frac{1}{2}$
$P(X=2)=P(T)×P(H)=\frac{1}{2}×\frac{1}{2}=\frac{1}{4}$
$P(X=3)=P(T)×P(T)×P(H)=\frac{1}{2}×\frac{1}{2}×\frac{1}{2}=\frac{1}{8}$
$P(X=4)=P(T)×P(T)×P(T)×(P(T)×P(H))=\frac{1}{2}×\frac{1}{2}×\frac{1}{2}×(\frac{1}{2}×\frac{1}{2})=\frac{1}{8}$