Question

Sasha wrote each of the numbers 21 through 40 on a different index card. She will randomly pick one card. A is the event of picking a number that is divisible by 3. B is the event of picking a prime number.

Answer 1

`Pr(A\ or\ B) = (1)/(2)`

Explanation:

Given

`S = \{21,22,23,24,......40\}`

`n(S) = 20`

`A = \{21,24,27,30,33,36,39\}` -- Divisible by 3

`B = \{23, 29, 31, 37\}` --- Prime numbers

Required

`Pr(A\ or\ B)`

This is calculated as:

`Pr(A\ or\ B) = Pr(A) + Pr(B) - Pr(A\ n\ B)`

Using probability formula, we have:

`Pr(A\ or\ B) = (n(A) + n(B) - n(A\ n\ B))/(n(S))`

Where:

`A = \{21,24,27,30,33,36,39\}`

`n(A) = 7`

`B = \{23, 29, 31, 37\}`

`n(B) = 4`

`A\ n\ B =\{\}`

`n(A\ n\ B) = 0`

So:

`Pr(A\ or\ B) = (n(A) + n(B) - n(A\ n\ B))/(n(S))`

`Pr(A\ or\ B) = (7 + 3 - 0)/(20)`

`Pr(A\ or\ B) = (10)/(20)`

`Pr(A\ or\ B) = (1)/(2)`