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?
Answers
Answer:
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}
100
50
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}
100
17
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}
100
7
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}
100
50
+
100
17
+
100
7
=0.740.74
Hence the probability that the number chosen is a multiple of 2 or 3 or 5 is 0.7