A number is chosen at random from the set S = 1, 2, 3, , 300 . Let A be the event that the chosen number is a multiple of 3 or 4 , and let B be the event that the chosen number is a multiple of 12 but not a multiple of 15 . The conditional probability P(B A) is equal to

Step-by-step solution

The sample space S contains 300 integers. Let n(k) denote the number of multiples of k in S . n(3) = 300 3 = 100 n(4) = 300 4 = 75 n(12) = 300 12 = 25 Event A is the set of numbers divisible by 3 or 4 . By the Principle of Inclusion-Exclusion: n(A) = n(3) + n(4) - n(12) = 100 + 75 - 25 = 150 . Event B is the set of numbers divisible by 12 but not by 15 . Notice that any number divisible by 12 is automatically divisible by both 3 and 4 , which means it is an element of A . Therefore, B A , and A B = B . To find n(B)