Question

Suppose we pick three people at random. For each of the 2.32 The following questions, ignore the special case where someone might be born on February 29th, and assume that births are evenly distributed throughout the year.(a) What is the probability that the first two people share a birthday?(b) What is the probability that at least two people share a birthday?

Answer 1

Answer:

(a) 1 in 365 or 0.2740%

(b) 0.8227%

Step-by-step explanation:

(a) For any given birthday date of the first person, there is a 1 in 365 chance that the second person shares the same birthday, therefore the probability that the first two people share a birthday is:

$P = \frac{1}{365}=0.2740\%$

(b) There are four possibilities that at least two people share a birthday, first and second, first and third, second and third, all three share a birthday. Therefore, the probability that at least two people share a birthday is:

$P =3* \frac{1}{365}+ (\frac{1}{365})^2\\ P=0.8227\%$