Question

One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6?

Solution

Let A be the event of choosing a number divisible by 4 ∴A=4,8,....,100 ⇒n(A)=25 P(A)=25100 Let B be the event of choosing a number divisible by 6 ∴B=6,12,...,96 ⇒n(B)=16 P(B)=16100 (A∩B)=12,24,.....,96 ⇒n(A∩B)=8 ∴P(A∩B)=8100 ∴P(A∪B)=P(A)+P(B)−P(A∩B) =25100+16100−8100=33100

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