The probability is:
0.013549
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:
[tex]\dfrac{1}{365}[/tex]
( 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:
[tex]\dfrac{364}{365}[/tex]
( 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:
[tex]=5\times (\dfrac{1}{365}\times (\dfrac{364}{365})^4)\\\\=5\times (\dfrac{364^4}{365^5})\\\\=0.013549[/tex]
