Answer
$P(X=5)=C(5,5)*0.1^5*0.9^0=\frac{5!}{5!\times(5-5)!}\times0.1^5\times0.9^0=0.00001$
The probability is $0.00001$
Work Step by Step
The solution is based on the binomial distribution:
$P(X=x)=C(n,x)*p^{x}*q^{n-x}$
If we perform 5 independent Bernoulli trials, and $p=0.1$, the probability of five successes are:
$C(5,5)*0.1^5*0.9^0$.
As there are 5 trial out of which all are successes. And the probability of a success is 0.1.
$P(X=5)=C(5,5)*0.1^5*0.9^0=\frac{5!}{5!\times(5-5)!}\times0.1^5\times0.9^0=0.00001$
