Answer
$0.0729$
Work Step by Step
Step 1. Identify the given quantities: $p=0.9, q=0.1, n=5, r=3$
Step 2. The probability $P(n,r)$ is given by the term containing $p^r$ in the binomial expansion of $(p+q)^n$,
thus we have $P(n,r)=\begin{pmatrix} n\\r \end{pmatrix}p^r q^{n-r}$
Step 3. Plug-in the numbers, we have:
$P(5,3)=\begin{pmatrix} 5\\3 \end{pmatrix}0.9^3 0.1^{5-3}=10\times 0.729 \times0.01=0.0729$ or $7.29\%$
