Question

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

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{8}$
• D. $\frac{3}{8}$

Answer 1

The correct option is A

$\frac{1}{2}$

$n=100,p=q=\frac{1}{2}\therefore p\text{(x-an odd number)}=p(x=1)+p(x=3)..............+p(x=99)=\frac{{}^{100}{c}_1{+}^{100}{c}_3..............{+}^{100}{c}_{99}}{2^{10}}=\frac{1}{2}$