Question

Ashmita and Shreya are sisters, what is the probability that both have a birthday on 14 September(ignoring leap year).

Answer 1

Hint:First, proceeding for this, we must know the total number of days in a year is 365. Then, we need to find the total number of ways by which the day is selected from a total of 365 days for both the sisters are $365\times 365={{365}^{2}}$. Then, we are clearly given the date as 14 September from 365 to be the date on which both of the girls are having their birthday which gives the required probability.

Complete step by step answer:
In this question, we are supposed to find the probability that both the sisters have a birthday on 14 September(ignoring leap year).
So, before proceeding for this, we must know the total number of days in a year is 365.
Then, we need to find the total number of ways by which the day is selected from a total of 365 days for both the sisters are:
$365\times 365={{365}^{2}}$
Now, we are clearly given with the date as 14 September from 365 to be the date on which both of the girls are having their birthday.
So, by using this condition, we get a favorable number of cases that is the day on which birthday can lie is 1.
Now, by using the concept of probability which says that it is the ratio of the favorable outcomes to the total outcomes.
So, by using the concept of probability, we get the probability of both the girls having their birthday on 14 September as:
$\dfrac{1}{{{365}^{2}}}$
Hence, we get the answer as $\dfrac{1}{{{365}^{2}}}$.

Note:
 Now, to solve these type of the questions we need to be careful with the conditions given in the question as it is clearly mentioned that do not assume it as leap year because if we take the condition of leap year then the total number of days in one-year changes to 366 and it will entirely change our answer.