Question

One number is chosen randomly from the integers 1 to 50. Find the probability that it is divisible by 4 or 6.
A) $\dfrac{4}{50}$
B) $\dfrac{8}{25}$
C) $\dfrac{4}{25}$
D) None

Answer 1

Hint: In this question it is given that we have to find the probability of a randomly chosen number between 1 to 50, which is divisible by 4 or 6. So to find the solution we have to first find how many integers are there which is divisible by 4 or 6 and we call this as the number of favourable outcomes.
So for this 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
E: ‘choosing an integer which is divisible by 4 or 6’.

Now the numbers of integers from 1 to 50 are 1,2,3,4,5,.....50.
So, Total number of outcomes =50.
Now , the numbers which are divisible by 4 are : 4,8,12,16,20,24,28,32,36,40,44,48.
And the numbers which are divisible by 6 are: 6,12,18,24,30,36,42,48.
That is, we have intotal 16 numbers which are divisible by 4 or 6.
So we can say that the number of possible events E is 16.

Now, the probability of choosing an integer which is divisible by 4 or 6, i.e,
P(E)=$\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$=$\dfrac{16}{50}$=$\dfrac{8}{25}$.
Which is our required solution.
Hence, the correct option is option B.
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.
Also in this question the event is choosing an integer which is divisible by 4 or 6, that means that you have to find all of those numbers which are either divisible by 4 or divisible by 6.