Question

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

• A. $\frac{1}{32}$
• B. $\frac{1}{2}$
• C. $\frac{3}{2}$
• D. $\frac{1}{5}$

Answer 1

The Correct Option is B

Let A be the event of getting tail in first four trial and B be the event of getting head in fifth trial. $\therefore P\left(A\right) = \left(\frac{1}{2}\right)^{4} P\left(B\right) = \left(\frac{1}{2}\right)^{5} $ $\because P\left(A \cap B\right) = P\left(A\right).P\left(B\right) = \left(\frac{1}{2}\right)^{5} $ $\because$ A and B are independent events $\therefore$ Probability of head appearing on fifth toss equal. $P\left(\frac{B}{A}\right) = \frac{P\left(A\cap B\right)}{P\left(A\right)\times P\left(B\right)} = \frac{\left(\frac{1}{2}\right)^{5}}{\left(\frac{1}{2}\right)^{4}} = \left(\frac{1}{2}\right)$