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Question

Answers

A. \[\dfrac{1}{4}\]

B. \[\dfrac{1}{2}\]

C. \[\dfrac{{25}}{{98}}\]

D. \[\dfrac{1}{3}\]

Answer

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As we know that we are asked the probability of numbers which are divisible by 1 and itself only.

So as per the definition of prime and composite numbers prime numbers are those numbers which are only divisible by 1 and the number itself like 2, 3, 5 etc. While the composite numbers are those which are divisible by 1, number itself and any other number also like 4, 6, 8 etc.

So, we had to find the probability of getting a prime number between 1 and 100.

Now as we know that the according to the probability formula probability of getting a favourable outcome \[ = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}\].

So here favourable outcome is prime number between 1 and 100.

As we know that there are a total of 98 numbers between 1 and 100 i.e. {2, 3, 4, 5, 6, …….. 95, 96, 97, 98, 99}.

So, now as per the above definition of prime numbers, the prime numbers between 1 and 100 will be {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}.

So, there are a total of 25 prime numbers between 1 and 100.

And there are 98 total numbers between 1 and 100.

So, probability of getting a prime number between 1 and 100 = \[\dfrac{{{\text{Number of prime numbers between 1 and 100}}}}{{{\text{Total number of numbers between 1 and 100}}}}\]

Probability of getting a prime number between 1 and 100 = \[\dfrac{{25}}{{{\text{98}}}}\]