JEE 2024 — Mathematics PYQ

U = {1, 2, 3.......50}

A = Set of integers which is multiple of 4
B = Set of integers which is multiple of 6
C = Set of integers which is multiple of 7

n(A) = 12
n(B) = 8
n(C) = 7

n(A ∩ B) = 4
n(B ∩ C) = 1
n(C ∩ A) = 1

n(A ∩ B ∩ C) = 0

$\therefore n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(C\cap A)+n(A\cap B\cap C)$
$=12+8+7-4-1-1+0$
$\therefore$ required probability
$=\frac{21}{50}$