When performing a binomial probability experiment the probability of having X succeses in n tries with a succes probability p is given by the following formula:
[tex]P(X)=\frac{n!}{X!\cdot(n-X)!}\cdot p^X\cdot(1-p)^{n-X}[/tex]Then in order to find the probability we just need to take n=40, p=0.97 and X=38:
[tex]\begin{gathered} P(X)=\frac{n!}{X!\cdot(n-X)!}\cdot p^X\cdot(1-p)^{n-X} \\ P(38)=\frac{40!}{38!\cdot(40-38)!}\cdot0.97^{38}\cdot(1-0.97)^{40-38} \\ P(38)=\frac{39\cdot40}{2!}\cdot0.314\cdot0.03^2 \\ P(38)=780\cdot0.314\cdot0.0009 \\ P(38)=0.220428 \end{gathered}[/tex]And if we round two decimal places we have that:
[tex]P(38)=0.22[/tex]