Question

If I am in a room with 5 people and guess all their birthdays what is the probability of getting (only) one correct?

Answer 1

The probability is:

0.013549

Explanation:

There are 5 people in a room.

Now the number of ways such that he get only one guess correct is: 5

Also, the probability of getting a correct guess is:

`(1)/(365)`

( Since, there are total 365 days in a year out of which one of day will be the day a person is born)

and the probability of getting a wrong guess is:

`(364)/(365)`

( Since, there are total 365 days in a year out of which one of day will be the day a person is born and the rest 364 days will be the day a person is not born )

Hence, the probability of getting (only) one correct is:

`=5* ((1)/(365)* ((364)/(365))^4)\\\\=5* ((364^4)/(365^5))\\\\=0.013549`