Question

Choose any whole number from 20 -> 400 at random. Compute the probability that it is divisible neither by 10 nor by 15

Answer 1

Total No. of numbers from 20 to 400 (inclusive) =n =400 - 19 =381

The numbers between 20 and 400 (inclusive) that are divisible by 10 are: 20, 30, 40,......................, 390 and 400.

A =No. of numbers that are divisible by 10 =39

The numbers between 20 and 400 (inclusive) that are divisible by 15 are: 30, 45, 60,............., 375 and 390.

B =No. of numbers that are divisible by 15 =25

The numbers between 20 and 400 (inclusive) that are divisible by both 10 and 15 are: 30, 60, 90,................, 360 and 390.

A and B =No. of numbers that are divisible by 15 =13

Let the probability =P

A Or B =A + B - A and B =39 + 25 - 13 =51

Neither A nor B =n - A or B =381 - 51 =330

The probability that any whole number drawn from 20 to 400 at random is divisible neither by 10 nor by 15 =P(neither A nor B) =330/381 =0.8661