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 eve…

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asked Apr 9, 2022 66.0k views

1 Answer

Danielspaniol · Answer 1 · 2022-04-13T06:03:02+0000

Answer:

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

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:

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

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

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

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