ANSWER:
The probability is 0.018
STEP-BY-STEP EXPLANATION:
That 5% are defective means that 5 out of 100 tires are defective.
If 5 tires are selected, the probability that they are exactly defective is calculated as follows
[tex]\begin{gathered} P(X=k)=\frac{5Ck\cdot95C5-k}{100C5},\text{ for k = 2} \\ \end{gathered}[/tex]Now, resolving
[tex]\begin{gathered} 5C2=\frac{5!}{2!\cdot(5-2)!}=10 \\ 95C3=\frac{95!}{3!\cdot(95-3)!}=138415 \\ 100C5=\frac{100!}{5!\cdot\left(100-5\right)!}=75287520 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} P(X=2)=\frac{10\cdot138415}{75287520} \\ P(X=2)=0.018 \end{gathered}[/tex]