An integer is chosen at random from the first 50 integers. What is the probability that the integer is neither divisible by 5 nor 9?

Step-by-step solution

Total number of integers in the sample space, n(S) = 50 . Let A be the event that the chosen integer is divisible by 5 , and B be the event that it is divisible by 9 . The number of integers divisible by 5 is n(A) = 10 . The number of integers divisible by 9 is n(B) = 5 . The number of integers divisible by both 5 and 9 (i.e., divisible by 45 ) is n(A B) = 1 . The number of integers divisible by either 5 or 9 is given by: n(A B) = n(A) + n(B) - n(A B) = 10 + 5 - 1 = 14 The number of integers neither divisible by 5