If a fair coin is tossed 20 times and let we get head $n$ times, then probability that $n$ is odd, is

Question

Dr. Abubacker · Accepted Answer

(a)
Probability of getting head in one trial, $P = \frac{1}{2}$ and probability of not getting head, $q = \frac{1}{2}$
Probability of getting head odd times
$= \ ^{26}C_{1}\left( \frac{1}{2} ight)^{1}\left( \frac{1}{2} ight)^{19} + \ ^{20}C_{3}\left( \frac{1}{2} ight)^{3}\left( \frac{1}{2} ight)^{17} + ... + \ ^{20}C_{19}\left( \frac{1}{2} ight)^{1}\left( \frac{1}{2} ight)^{19}$
$= \frac{1}{2^{20}}\left\lbrack \ ^{20}C_{1} + \ ^{20}C_{3} + ... + \ ^{20}C_{19} ightbrack$
$= \frac{1}{2^{20}} 	imes 2^{20 - 1}$
$= \frac{2^{19}}{2^{20}} = \frac{1}{2}$

Q. If a fair coin is tossed 20 times and let we get head $n$ times, then probability that $n$ is odd, is

Explanation

Reviewed by Dr. Abubacker

Want more practice?