Question

A coin is tossed three times. If $X$ denotes the absolute difference between the number of heads and the number of tails then $P(X=1)=$

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{1}{6}$
• D. $\frac{3}{4}$

Answer 1

Answer: (D)

$\frac{3}{4}$

Following cases are possible,

1 head 1 head 1 tail, 1 head 1 tail 1 head, 1 tail 1 head 1 head, 1 tail 1 tail 1 head, 1 tail 1 head 1 tail, 1 head 1 tail 1 tail

probability of each event is,

$\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}$

Hence total probability is,

$=\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}$

$=\frac{3}{4}$