Question

An integer is chosen at random from the first 100 integers. What is the probability that this number will not be divisible by 5 or 8?

Answer 1

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p(e) = 0.3

,....................

Answer 2

Given,

Total numbers  = 100

To Find,

The probability that a randomly choosen number will not be divisible by 5 or 8 =?

Solution,

First 100 integers are 1,2,3,4,...........,100

Sample space = 100

Numbers divisible by 8 between 1 - 100,

8,16,24,32,40,48,56,64,72,80,88,96

Numbers divisible by 5 between 1 - 100,

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

Total numbers divisible by 5 or 8 = 30

Probability of getting a number divisible by 5 or 8 = 30 / 100

Probability of getting a number not divisible by 5 or 8 = 1 - 30 / 100

Probability of getting a number not divisible by 5 or 8 =  1 - 3 / 10

Probability of getting a number not divisible by 5 or 8 =  (10 - 3) / 10

Probability of getting a number not divisible by 5 or 8 =  7 / 10

Hence, the probability of getting a number not divisible by 5 or 8 is

7 / 10.