Question

An unbiased coin is tossed 32 times . Find the probability of obtaining 2 heads .

Answer 1

$n=32$

$p=$ success$=$probability of getting head in me toss

$=\frac{1}{2}$

$q=1-p=\frac{1}{2}$

$x=$ no. of heads obtained

$\therefore P(x=2)=$ required probability

$={}^{32}{C}_2{\left(\frac{1}{2}\right)}^2{\left(\frac{1}{2}\right)}^{30}$

$=\frac{32!}{30!2!}{\left(\frac{1}{2}\right)}^{32}$

$=32\times 31\times \frac{1}{2^{32}}=31\times \frac{1}{2^{27}}$.