Question

a natural number is chosen at random from among the first 500 what is the probability that number so chosen is divisible by 3 or 5​

Answer 1

Step-by-step explanation:

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.