GATE ECE 2012 | Question: 36

Question

A fair coin is tossed till head appears for the first time. The probability that the number of required tosses is odd, is

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

Answer 1

Probability of getting head = $\frac{1}{2}$

Probability of not getting head = probability of getting tail = $\frac{1}{2}$

Coin is tossed odd number of times untill it’s get first head,

i.e., required outcomes of these trials = {$H,TTH,TTTTH,...$}

So, required probability of getting these outcomes $= \frac{1}{2}+(\frac{1}{2})^3+(\frac{1}{2})^5+….$

$$=\frac{\frac{1}{2}}{1-\frac{1}{4}}=\frac{2}{3}$$

Correct Answer: $C$