Probability is the ratio of: the number of observations of an event n(A) compared to the total number of observation n(S). Generally it could be written as P(A) = [tex] \dfrac{n(A)}{n(S)}[/tex]
Use combination to solve this problem The event being observed n(A) in this problem is 2 engineers being selected from 4 engineers. The observation n(S) is about 2 people being selected from 10 people (engineers + pilots).
n(A) could be determined using combination of 2 engineers from 4 engineers n(A) = [tex]C^4_2[/tex] n(A) = [tex]\dfrac{4!}{2!(4-2)!}[/tex] n(A) = [tex]\dfrac{4!}{2!2!}[/tex] n(A) = [tex]\dfrac{4 \times 3 \times 2 \times 1}{2 \times 1 \times 2 \times 1}[/tex] n(A) = [tex]\dfrac{24}{4}[/tex] n(A) = 6
n(S) could be determined using combination of 2 people from 10 people n(S) = [tex]C^10_2[/tex] n(S) = [tex]\dfrac{10!}{2!(10-2)!}[/tex] n(S) = [tex]\dfrac{10!}{2!8!}[/tex] n(S) = [tex]\dfrac{10 \times 9 \times 8!}{2 \times 1 \times 8!}[/tex] n(S) = [tex]\dfrac{10 \times 9}{2}[/tex] n(S) = [tex]\dfrac{90}{2}[/tex] n(S) = 45
The probability P(A) = [tex] \dfrac{n(A)}{n(S)}[/tex] P(A) = [tex] \dfrac{6}{45}[/tex] P(A) = [tex] \dfrac{2}{15}[/tex]
