Question

A fair coin is tossed 19 times. Let x be the number of times head occurs. Then p (x=r) is maximum when r is

• A. 9
• B. 12
• C. 11
• D. 8

Answer 1

Answer: (A)

9

Answer 2

If head occurs r times, then

P(when x = r) = $19C_{r}\left( \frac{1}{2} \right)^{r}\left( \frac{1}{2} \right)^{19 - r} =^{19}C_{r}\left( \frac{1}{2} \right)^{19}$

P(x = r) is maximum, when $19C_{r}$ is maximum.

It is maximum when r = 9 or 10.

(Since in a binomial expansion, middle term has greatest coefficient.)