Question

A number is drawn from the first 30 natural numbers and it appears to be an odd number. Find the probability of the number so drawn being a prime number.

Answer 1

Hint: Focus on the point that there are 15 odd numbers lying in the first 30 natural numbers, out of which 9 are primes. So, the number of favourable outcomes for the mentioned situation is 9 and total outcomes is 15.
Probability in simple words is the possibility of an event to occur.
Probability can be mathematically defined as $=\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$ .
Complete step-by-step answer:
It is given in the question that the drawn number is odd and we know that among the first 30 natural numbers half are odd and half are even. So, there are 15 odd numbers which is our total number of outcomes for the above mentioned question. Also, we know out of these 15 odd numbers, there are 9 primes.
The numbers which are divisible by 1 and the number itself and doesn’t have any other factors are known as prime numbers. So, the numbers which are prime, less than 30 and odd are: 3, 5, 7, 11, 13, 17, 19, 23, 29. So, the favourable outcomes for the above mentioned situation is 9.
Therefore, the probability of the number so drawn being a prime number, provided the number drawn is an odd number is:
$\operatorname{}\text{Probability}=\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}=\dfrac{9}{15}=\dfrac{3}{5}$
Therefore, the answer to the above question is $\dfrac{3}{5}$ .

Note: It is preferred that while solving a question related to probability, always cross-check the possibilities, as there is a high chance you might miss some or have included some extra or repeated outcomes. Also, when a large number of outcomes are to be analysed then permutations and combinations play a very important role. Also, for the above question don’t get confused and consider 2 also as a favourable case, as 2 is a prime number, but it is not odd.