Answer
$P(X=0)=C(5,0)*0.1^0*0.9^5=\frac{5!}{0!\times(5-0)!}\times0.1^0\times0.9^5=0.59049$
The probability is $0.59049$
Work Step by Step
The solution is based on the binomial distribution:
$P(X=x)=C(n,x)*p^{x}*q^{n-x}$
All failures means no successes
If we perform 5 independent Bernoulli trials, and $p=0.1$, the probability of zero successes are:
$C(5,0)*0.1^0*0.9^5$.
As there are 5 trial out of which none is a success. And the probability of a success is 0.1.
$P(X=0)=C(5,0)*0.1^0*0.9^5=\frac{5!}{0!\times(5-0)!}\times0.1^0\times0.9^5=0.59049$
