Let A be the event that a randomly selected two digit number is divisible by 3 and let B be the event that a randomly selected two digit number is divisible by 5. What is P(A and B)?

A. 1/18
B. 1/15
C. 1/5
D. 1/3
E. 1/2

We know that

P(A and B) = P(A) * P(B)

Event where a two digit no is divisible by 3 => 30 (12 to 99)
Total two digit no.s = 90
Hence P(A) = 30/90 => 1/3

Similarly, Event where a two digit no is divisible by 5 => 18 (10 to 95)
P(B) = 18/90 => 1/5

P(A and B) = 1/3 * 1/5 => 1/15

Option B

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Let A be the event that a randomly selected two digit number is divisible by 3 and let B be the event that a randomly selected two digit number is divisible by 5. What is P(A and B)?

A. 1/18
B. 1/15
C. 1/5
D. 1/3
E. 1/2

The event A and B means that a randomly selected two digit number is divisible by both 3 and 5. Since the least common multiple of 3 and 5 is 15, that event is same as a randomly selected two digit number is divisible by 15.

The total number of two digit number is 90(from 10 to 99 inclusively). The number of the multiples of 15 from 10 to 99 is [100/15]=6.

So P(A and B) = 6/90 = 3/45 = 1/15. So the answer is B.
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