Question

What is the probability that two friends have the same birthday?
A.\[\dfrac{{364}}{{365}}\]
B.\[\dfrac{{363}}{{365}}\]
C.\[\dfrac{{365}}{{365}}\]
D.\[\dfrac{1}{{365}}\]

Answer 1

Hint: In this question, we know that the birthday comes only once a year so we will find the probability of the occurrence of birthday for one friend and that day will be same for the birthday of the other friend.

Complete step-by-step answer:
We know that there are 365 days in a year.
Now let us assume that the two friends have a birthday on the day x, where x can be any day in 365 days.
So the total number of our favourable outcome will be one since both the fiend have a birthday on the same date.
\[F.O = 1\]
Now since there are 365 days in a year and birthday can occur on any one day of the year; hence the total number of the outcome will be
\[T.O = 365\]
Now as we know the probability of an event to occur is the ratio of the favourable outcome by the total number of the outcome, hence we can say the probability that two friends have the same birthday
\[P(same) = \dfrac{{F.O}}{{T.O}} = \dfrac{1}{{365}}\]
Therefore, the probability that two friends have the same birthday \[ = \dfrac{1}{{365}}\]

So, the correct answer is “Option D”.

Note: A branch of mathematics which deals with numerical analysis of how likely an event is to occur, or the proportion is true. Probability of an event lies between 0 and 1, which means the chance of occurrence of an event increases as probability leads to 1 and if the probability is 0 for an event then there is no chance of occurrence of that event.