Question

If the probability that a person can swim is $0.4$. Five persons are selected randomly to jump into a river, then the probability that $2$ of them survive is

$\left(a\right)\frac{144}{625}\left(b\right)\frac{232}{625}$
$\left(c\right)\frac{108}{125}\left(d\right)\frac{216}{625}$

Answer 1

Let E be the event that the selected person can swim
Then,
$p=P\left(E\right)=0.4=\frac{2}{5}q=P\left(\overline{E}\right)=1-0.4=0.6=\frac{3}{5}$

Now, according to the question if two people survive that means only two of them are swimmers
Here $n=5,x=2$
Then, the probability that only two of them survive is
$P(X=2)={}^n{C}_x\left(p{)}^r\right(q{)}^{n-x}$
$={}^5{C}_2{\left(\frac{2}{5}\right)}^2{\left(\frac{3}{5}\right)}^3$
$=\frac{216}{625}$
Ans : $\left(d\right)$