Imagine you have 2 brothers and 3 sisters. What is the probability that at least 2 of you have the same birthday.
I am getting .00274...which is NOT what the book has. Please explain your answer so I can learn how this is done.
2007-07-10 13:41:50 · 1 answers · asked by C K 3 in Science & Mathematics ➔ Mathematics
If you have 2 brothers and 3 sisters, that's six people in total. We can assume that each of these six people was born on a random date (obviously this is not how actual biology works, but whatever). If there are 365 possible birthdays, the probability that at least two people have the same birthday is simple 1 minus the probability that nobody shares a birthday. Calculating the probability that nobody shares a birthday is simple:
The first person has a birthday, with a probability of 1.
The probability that the second person does not have this birthday is 364/365.
The probability that the third person does not have either of the birthdays of the first two people is 363/365.
The probability that the fourth person does not have any of these three birthdays is 362/365.
And so on.
So, the probability that nobody shares a birthday is
P = (364/365) * (363/365) * (362/365) * (361/365) * (360/365)
P = 0.959538
Therefore, the probability that there is a shared birthday is
P = 1 - 0.959538
P = 0.0404625
which is hopefully the answer your book gives.
2007-07-10 13:53:17 · answer #1 · answered by lithiumdeuteride 7 · 1⤊ 0⤋