Question

A natural number is chosen at random from the first 100 natural numbers. what is the probability that the number chosen is a multiple of 2 or 3 or 5?

Answer 1

1...100
multiple of 2 (50)
multiple of 3 is 33
multiple of 5 is 20
use the formula p (a)÷N

Answer 2

Answer:

0.7

Step-by-step explanation:

First 100 natural numbers: {1,2,3,4,5......,100}

Multiples of 2 in first 100 natural numbers :

{2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100}=50

So, Probability of getting a multiple of two from 1 to 100 = $\frac{50}{100}$

Multiples of 3 in first 100 natural numbers :

{3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99} =33

Exclude the Multiples of 3 that are also a multiple of 2

{3,9,15,21,27,33,39,45,51,57,63,69,75,81,87,93,99} =17

So, Probability of getting a multiple of 3 from 1 to 100 = $\frac{17}{100}$

Multiples of 5 in first 100 natural numbers :

{5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100} =20

exclude the multiples of 2 and 3

{5,25,35,55,65,85,95} =7

So, Probability of getting a multiple of 3 from 1 to 100 = $\frac{7}{100}$

So, he probability that the number chosen is a multiple of 2 or 3 or 5 :

=$\frac{50}{100}+\frac{17}{100}+\frac{7}{100}$

=$0.74$

Hence the probability that the number chosen is a multiple of 2 or 3 or 5 is 0.7.