Problema Solution
Jack randomly chooses one of the positive integer divisors of 20, and Jill randomly picks one of the positive integer divisors of 30. What is the probability that Jack and Jill pick the same number? express your answer as a common fraction
Answer provided by our tutors
The positive integer divisors of 20 are: 1, 2, 4, 5, 10, 20 (6 divisors)
The positive integer divisors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30 (8 divisors)
The common divisors of 20 and 30 are: 1, 2, 5, 10 (4 divisors)
The total number of pickings is: 6*8 = 48
Jack and Jill can pick the same number: 4 times.
The probability is:
P(Jack and Jill pick the same number) = 4/48
P(Jack and Jill pick the same number) = 0.0833 or 8.33%