Question

There are 40 tickets numbered from 1 to 40, one ticket is drawn at random. Find the probability of getting (a) divisible by 4 and (b) prime numbers.

Answer 1

Hint:
Write the total number of tickets as the number of possible outcomes. For part (a), find the number of tickets divisible by 4 by dividing 4 by 40. In the next part, write the numbers which are prime from 1 to 40. Then, apply the formula of probability, $\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of possible outcomes}}}}$ to find the required probability.

Complete step by step solution:
Since, there are 40 tickets, we can say the total number of possible outcomes of getting a ticket in 40.
In part (a) we have to find the probability of getting a ticket divisible by 4.
The numbers that are divisible by 4 are $\dfrac{{40}}{4} = 10$ numbers
As we know that the probability of an event is calculated as $\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of possible outcomes}}}}$
On substituting the values, we will get,
$\dfrac{{10}}{{40}} = \dfrac{1}{4}$
In part (b), we have to find the probability of getting a prime number out of 40 tickets.
Prime numbers are the numbers that have only two factors, that are 1 and the number itself.
The prime numbers from 1 to 40 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.
That is, there are 12 prime numbers from 1 to 40.

Hence, the probability of getting a prime number from 1 to 40 is $\dfrac{{12}}{{40}} = \dfrac{3}{{10}}$

Note:
Many students take all the odd numbers as prime numbers, which is incorrect. For example, 9 is an odd number but has more than two factors, which are 1, 3 and 9. Also, 1 is neither a prime nor a composite number. Probability of any event cannot be less than 0 and cannot be greater than 1.