Choosing two math instructors out of 8 would be
[tex]P=\frac{2}{8}=\frac{1}{4}[/tex]Choosing two science instructors out of 10 would be
[tex]P=\frac{2}{10}=\frac{1}{5}[/tex]Given that they are independent events, we multiply their probabilities
[tex]P=\frac{1}{4}\times\frac{1}{5}=\frac{1}{20}[/tex]Hence, the probability of selecting two math instructors and two science instructors is 1/20.
