Birthdays: we are investigating to figure out how many persons may be in the same room, before the probability that at least 2 of them have the same birthday exceeds 1/2. Are you able to make a good guess at the answer in advance?

(a) Musa and Ibrahim wonder what the probability that the two are not born on the same date happens to be. Calculate this!

(b) Their common friend Issa found the answer, but he wonders what the probability that none of the three have the same birthday happens to be.

(c) What is the probability that at least two of them share a birthday.

(d) Math teacher Mohammed thinks the three have an interesting investigation, and wonders what the probability is if they include him as a fourth person. What is the probability that Musa, Ibrahim, Issa, and Mohammed all have different birthdays?

(e) What is the probability that at least two of the four share a birthday?

(f) Their fellow student Aisa tells them to finish their warm-ups, and go for the main question: How many persons can be present in a room before the probability that at least two of them have the same birthday exceeds 1/2? She hints that the answer is less than 30. What is answer to Aisa’s question?