Answer:
Step-by-step explanation:
Given that we pick up three people at random.
We can ignore the leap year so we assume there are 365 days in a year.
Probability for a person to be born on a specific data is equally likely and hence equal to
[tex]\frac{1}{365}[/tex]
Each person out of three persons is independent of the other.
Hence for the second person to have the same birthday would have equal probability.
X = No of persons to have common birthday is binomial with n =3 and p = [tex]\frac{1}{365}[/tex]
a) the probability that the first two people share a birthday
= [tex](\frac{1}{365})^2\\= \frac{1}{133225}[/tex]
b) the probability that at least two people share a birthday
= [tex]P(X\geq 2)\\=P(x=2)+P(x=3)\\= 3C2 (\frac{1}{365} )^2*\frac{364}{365}+(\frac{1}{365})^3[/tex]
