Question

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

• A. 1/3
• B. 1/2
• C. 2/3
• D. 3/4

Answer 1

The correct option is C 2/3

Number of tosses	Outcome	Required Probability
1	H	$\frac{1}{2}$
3	TTH	${\left(\frac{1}{2}\right)}^3$
5	TTTTH	${\left(\frac{1}{2}\right)}^5$
...	...	...

Required Probability

$=\frac{1}{2}+{\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{2}\right)}^5+...$

$=\frac{\frac{1}{2}}{1-{\left(\frac{1}{2}\right)}^2}=\frac{\frac{1}{2}}{\frac{3}{4}}$

$=\frac{2}{3}$