Q. $A$ and $B$ toss a coin alternately on the understanding that the first to obtain head win the toss. The probability that $A$ wins the toss
A) $\frac{1}{3}$
B) $\frac{2}{3}$
C) $\frac{1}{4}$
D) $\frac{3}{4}$
Explanation
(b)
$P(H) = P(T) = \frac{1}{2}$
$\therefore$ Required probability $= P(A) + P\left( \overline{A} \cap \overline{B} \cap A \right) + ...$
$= \frac{1}{2} + \left( \frac{1}{2} \right)^{3} + \left( \frac{1}{2} \right)^{5} + ... = \frac{\frac{1}{2}}{1 - \frac{1}{4}} = \frac{2}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.