Question

A fair coin is tossed repeatedly. If the tail appears on the first four tosses then the probability of the head appearing on the fifth toss equals

• A. $\frac{1}{2}$
• B. $\frac{1}{32}$
• C. $\frac{31}{32}$
• D. $\frac{1}{5}$

Answer 1

The correct option is A

$\frac{1}{2}$

Explanation for the correct option:

A fair coin tossed repeatedly

The probability of the head appearing on the fifth toss is equal to the probability of the tail appearing on the fifth toss.

Total number of outcomes $=\left\{H,T\right\}$

Chances of getting head $=1$

Probability of getting head $=\frac{\mathbf{1}}{\mathbf{2}}\left[\because \mathrm{Probability}=\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}\right]$

Hence, Option(A) is the correct answer.