Question

A natural number chosen at random from among the first 500. What is the probability that the number so chosen is divisible by 3and 5

Answer 1

ans
33/500
hope answer will help you

Answer 2

The number chosen at random which is divisible by 3 and 5 among the first 500 natural numbers is 0.066.

• Given numbers are 1 to 500.

• A random number chosen must be divisible by 3 and 5.

• We know that, if a number is divisible by 3 and 5, then it must be divisible by 15.

• So if we find the number of digits divisible by 15, we can know the number of events possible.

First number divisible by 15 = 15,

Last number divisible by 15 that i less than 500 = 495

• We have to find the number of terms in between them,

Common difference = 15

495 = 15 + ( n - 1 ) 15   [ Nth term formula of an AP ]

495 - 15 =  15 ( n - 1 )

480 = 15 ( n - 1 )

480 / 15 = ( n - 1 )

32 = ( n - 1 )

n = 32 + 1 = 33

• So Total number of such terms divisible by 3 and 5 is 33 out of 500.

• Probability can be calculate by

P = n(E) / n(S)

Here, n(E) = 33, n(S) = 500

P = 33 / 500 = 0.066

• Hence the number chosen at random which is divisible by 3 and 5 is 0.066.