Question

what is the probability that a number randomly selected from the first 500 natural numbers is a multiple of 2 or 3 or 5.

Answer 1

First 500 natural nos. are:

1,2,3,4,5,6,7,8,9,10..........500

From these the multiples of 2 are:

2,4,6,8,10,12.....500

This is in an AP

500=2+(n-1)2

n=250

∴There are 250 multiples of 2

NOW,

Multiples of 3:

3,6,9,12,15,18..........498

498=3+(n-1)3

n=166

Therefore there are 166 multiples of 3 b\w 1 and 500

Now the multiples of 5

5,10,15,20.........500

500=5+(n-1)5

n=100

Therefore there are 100 multiples of 5 b\w 1 and 500

NOW THE MULTIPLES OF 2,3 AND 5 WHICH OVERLAP ARE:

30,60,90..........480,

480=30+(n-1)30

n=16

Therefore there are 16 multiples of 2,3 and 5 which overlap each other

P(E)getting a multiple of 2 or 3 b\w 1 and 500 is = (250+166+100)-16

                                                                                    =500

P(E)           ||                                                                  =500\500=1

Hope it helps

Mark it as brainliest plzz.