find the probability that n people (n<365) selected at random will have n different birthdays.
Answers
Answer:
We assume that there are only 365 days in a year and that all birthdays are equally probable, assumptions whichare not quite met in reality.The first of the npeople has of course some birthday with probability 365365 1. Then, if the second is tohave a different birthday, it must occur on one of the other 364 days. Therefore, the probability that the secondperson has a birthday different from the first is 364365. Similarly the probability that the third person has abirthday different from the first two is 363365. Finally, the probability that the nth person has a birthday>>>1e10.6321112!13!c1e1e11a112!13!cbex1xx22!x33!c112!13!c(1)n11n!c(1)n1annb a1n!bP(A1<A2<c<An)an1b a1nban2b a1nb a1n1ban3b a1nb a1n1b a1n2bCHAPTER 1Basic Probability26different from the others is (365 nl)365. We therefore haveP(allnbirthdays are different)