Question

How many integers from 1 through 1,000 are multiples of 5 or multiples of 9?

(b)

Suppose an integer from 1 through 1,000 is chosen at random. Use the result of part (a) to find the probability that the integer is a multiple of 5 or a multiple of 9. (Round to the nearest tenth of a percent.)

(c)

How many integers from 1 through 1,000 are neither multiples of 5 nor multiples of 9?

Answer 1

a) If A and B be no of integers multiple of 5 and 18 respectively, then:
Integers multiple of 5, A = {5,10,15......,1000} => n(A) = 200

Integers multiple of 9, B = {9,18, 27,......999}. => n(B) = 111

Integers multiple of both 5 and 9 are the integers multiple of 45. So the event (A and B) is the numbers multiple of 45. So, (A and B) = { 45, 90, 135, ...990} => n(A and B) = 22

If E be the event that a number is multiple of 5 or 9, then E = A or B

So, n(E) = n(A) + n(B) - n(A and B) = 200 + 111 - 22 = 289

b) Pr (No is multiple of 5 or 9) = P(E) = n(E)/n(Total) = 289/1000 = 0.289 = 28.9%

c) No of integers which are neither multiple of 5 nor 9 = 1000 -no of integer which are multiple of 5 or 9

= 1000 - 289 = 711