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Q.

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

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a

6 50  

b

43 49  

c

6 49  

d

3 4   

answer is B.

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Detailed Solution

Given that the number of integers ranges between 1 to 100.
We need to find the probability that if a number is chosen, it is not divisible by 8.
Probability of an event E is defined as:
P(E)=Number of favorable outcomesTotal number of possible outcomes
We have numbers between 1 to 100.
Therefore, the total number of possible outcomes is 98.
Numbers divisible by 8 are:
8,16,24,32,40,48,56,64,72,80,88,96
So, there are 12 numbers that are divisible by 8.
Thus, the number of favorable outcomes will be:
98−12=86  
Let E   be the event that the number is not divisible by 8.
Now, the probability of getting a number not divisible by 8 is:
P(E)= 86 98 ⇒P(E)= 43 49  
The probability of getting a number not divisible by 8 is 43 49  .
Therefore, option 2 is correct.
 
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