Question

A fair coin is tossed 100 times. The probability of getting tails an odd number of times is

• A. $\frac { 1 } { 2 }$
• B. $\frac { 1 } { 8 }$
• C. $\frac { 3 } { 8 }$
• D. None of these

Answer 1

Answer: (A)

$\frac { 1 } { 2 }$

Answer 2

The total number of cases are $2 ^ { 100 }$

The number of favourable ways

${ } ^ { 100 } C _ { 1 } + { } ^ { 100 } C _ { 3 } + \ldots \ldots . + { } ^ { 100 } C _ { 99 } = 2 ^ { 100 - 1 } = 2 ^ { 99 }$

Hence required probability