Question
Mathematics Question on Slope of a line
From a set of 100 cards numbered 1 to 100, one card is drawn at random. Find the probability that the number obtained on the card is divisible by 6 or 8, but not by 24.
A
(A) 625
B
(B) 14
C
(C) 16
D
(D) 25
Answer
(A) 625
Explanation
Solution
Explanation:
E=set of numbers divisible by 6={6,12,18,24,30,…,96}F=set of numbers divisible by 8={8,16,24,…,96}E∩F=set of numbers divisible by 6 and 8={24,48,72,96}∴n(E)=16,n(F)=12,n(E∩F)=4∴n(E∪F)=n(E)+n(F)−n(E∩F)=16+12−4=24 and n(S)=100∴ Required probability=n(E∪F)n(S)=24100=625