Question

An integer is chosen at random between 1 and 100. Find the probability that it is not divisible by 8.

Answer 1

Hint: In this question it is given that an integer is chosen at random between 1 and 100. So we have to find the probability of that chosen integer which is not divisible by 8. So, to find the probability of choosing an integer which is not divisible by 8, we have to know that Probability =$$\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$$.
Where, the number of favourable outcomes is the number of ways that an event can happen.
Complete step-by-step solution:
So the event for this question is ‘choosing an integer which is not divisible by 8’.
Number of integers between 1 and 100 is 2,3,4,5,.....99.
So, Total number of outcome =98
Now , the numbers which are divisible by 8 are : 8,16,24,32,40,48,56,64,72,80,88,96.
That is, we have intotal 12 numbers which is divisible by 8.
So , the numbers which are not divisible by 8 = (98-12)=86
So, we can say that the number of possible event =86

Now, the probability of choosing an integer which is not divisible by 8, i.e,
P(not divisible by8)=$$\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$$=$$\dfrac{86}{98}$$=$$\dfrac{43}{49}$$.
Which is our required solution.
Note: To solve this type of question, firstly you have to know the probability formula and also you have to identify what is the event, by this you can easily find the number of ways for an event.