Question

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

विकल्प

• 1/2

• 1/8

• 3/8

• None of these

   

Answer 1

1/2
Here n=100
Let X denote the number of times a tail is obtained.

\[\text{ Here } , p = q = \frac{1}{2}\]
\[P(X = \text{ odd} ) = P(X = 1, 3, 5, . . . . 99) \]
\[ = \left( ^{100}{}{C}_1 + ^{100}{}{C}_3 + . . . . . + ^{100}{}{C}_{99} \right) \left( \frac{1}{2} \right)^{100} \]
\[ = \text{ Sum of odd coefficients in binomial expansion in}\   (1 + x )^{100} \left( \frac{1}{2} \right)^{100} \]
\[ = \frac{2^{(100 - 1)}}{2^{100}}\]
\[ = \frac{1}{2}\]