Question

Ashmita and Shreya are sisters, what is the probability that both have birthday on 14th September (ignoring the leap year)
A. $\dfrac{1}{{30}}$
B. $\dfrac{2}{{365}}$
C. $\dfrac{1}{{366}}$
D. $\dfrac{1}{{{{\left( {365} \right)}^2}}}$

Answer 1

Hint: This problem deals with probability, which is given by the ratio of the favorable outcome to the total number of outcomes. Here we have to find the probability that both sisters have their birthdays on the same day of the year, ignoring the leap year. A normal year has 365 days, whereas the leap year has 366 days.

Complete step-by-step solution:
Given that there are two sisters named Ashmita and Shreya.
We are asked to find the probability that both the sisters have their birthday on the same day which is mentioned here as 14th of September.
Here given to ignore the leap year.
Here probability of a favorable event is given by the ratio of the favorable outcome to the total no. of outcomes.
The probability that Ashmita has her birthday on 14th of September out of 365 days, is given by:
$ \Rightarrow \dfrac{1}{{365}}$
Now the probability that Shreya has her birthday on 14th of September out of 365 days, is given by:
$ \Rightarrow \dfrac{1}{{365}}$
Hence the probability that both the sisters have their birthdays on the same day which is on 14th of September, is given by the product of the probability that Ashmita has her birthday on 14th of September and the probability that Shreya has her birthday on 14th of September. Which is expressed mathematically below:
$ \Rightarrow \dfrac{1}{{\left( {365} \right)}} \times \dfrac{1}{{\left( {365} \right)}}$
$ \Rightarrow \dfrac{1}{{{{\left( {365} \right)}^2}}}$
Hence the probability that both the sisters have their birthday on 14th September is $\dfrac{1}{{{{\left( {365} \right)}^2}}}$
The probability is $\dfrac{1}{{{{\left( {365} \right)}^2}}}$.

Option D is the correct answer.

Note: This problem can be done in another method as well, where the other method is described here. The total no. of outcomes in the event is $365 \times 365$, as these are total no. of chances for both the sisters combined. The probability of the favorable outcome is 1 here, as both need to have their birthdays on the same day. Hence applying the formula of probability of the favorable event gives the same final answer.