discrete math please help 8 Find the probability of getting

8.) Find the probability of getting an integer not divisible by 5 or by 7 among all positive integers not exceeding 1000. Do not forget to write events (10pts.)

Solution

A = Number divisible by 5 = [1000/5] = 200

B = Number divisible by 7 = [1000/7] = 142

C = Number divisible by both 5 and 7 (number divisible by 35] = [1000/35] = 28

AUB = A + B - (A int B)

= A + B - C

= 200 + 142 - 28

= 314

Number not divisible by 5 or 7 = 1000 - 314 = 686

Hence Probability of getting an integer not divisible by 5 or 7

=> 686/1000 = 0.686