Answer:
[tex]Pr(A\ or\ B) = \frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]S = \{21,22,23,24,......40\}[/tex]
[tex]n(S) = 20[/tex]
[tex]A = \{21,24,27,30,33,36,39\}[/tex] -- Divisible by 3
[tex]B = \{23, 29, 31, 37\}[/tex] --- Prime numbers
Required
[tex]Pr(A\ or\ B)[/tex]
This is calculated as:
[tex]Pr(A\ or\ B) = Pr(A) + Pr(B) - Pr(A\ n\ B)[/tex]
Using probability formula, we have:
[tex]Pr(A\ or\ B) = \frac{n(A) + n(B) - n(A\ n\ B)}{n(S)}[/tex]
Where:
[tex]A = \{21,24,27,30,33,36,39\}[/tex]
[tex]n(A) = 7[/tex]
[tex]B = \{23, 29, 31, 37\}[/tex]
[tex]n(B) = 4[/tex]
[tex]A\ n\ B =\{\}[/tex]
[tex]n(A\ n\ B) = 0[/tex]
So:
[tex]Pr(A\ or\ B) = \frac{n(A) + n(B) - n(A\ n\ B)}{n(S)}[/tex]
[tex]Pr(A\ or\ B) = \frac{7 + 3 - 0}{20}[/tex]
[tex]Pr(A\ or\ B) = \frac{10}{20}[/tex]
[tex]Pr(A\ or\ B) = \frac{1}{2}[/tex]
