Question

If $1$ out of every $5$ ships sinks, then the probability that out of the $4$ ships departing from the shore, none of the ships sink is

$\left(a\right)\frac{64}{625}\left(b\right)\frac{256}{3125}$
$\left(c\right)\frac{256}{625}\left(d\right)\frac{1024}{3125}$

Answer 1

The probability that the ship sinks is, $p=\frac{1}{5}$
The probability that the ship does not sinks is, $q=\frac{4}{5}$

By using bernoulli trials,
$P(X=x)={}^n{C}_x{p}^x{q}^{n-x}$
Here, $n=4$ and $x=0$

$\therefore$ The probability that none of the departing ship sinks is,
$P(X=0)={}^4{C}_0{p}^0{q}^4$
$=1\times {\left(\frac{1}{5}\right)}^0\times {\left(\frac{4}{5}\right)}^4$
$=\frac{256}{625}$
Ans : $\left(c\right)$