In order to calculate this probability, we can use the formula:
[tex]P=C(n,x)\cdot p^x\cdot(1-p)^{n-x}[/tex]So, for n = 40, p = 0.03 and x = 2, we have:
[tex]\begin{gathered} C(40,2)=\frac{40!}{2!(40-2)!}=\frac{40\cdot39\cdot38!}{2!\cdot38!}=\frac{40\cdot39}{2}=780 \\ \\ P=780\cdot0.03^2\cdot0.97^{38} \\ P=0.2206 \end{gathered}[/tex]So the probability is 0.2206.
