Question

A die is a six-sided figure; each side shows a number of spots; the numbers of spots on the six sides are 1, 2, 3, 4, 5, and 6. Unless the problem says otherwise, you can assume that the die is fair, that is, each face has chance 1/6 of appearing regardless of what has appeared before.
a) Find the chance that the 5 people have 5 different birthdays.
b)A die is rolled three times. Find the chance that three different faces appear.

Answer 1

Both parts of the question ask you to find (I'm not sure that this is the right term) dependent probabilites. What I mean by that is that once you have used one of the outcomes, you can't use it again, so you remove it from the pile of possibilites. I doubt that makes much sense, but it's kind of hard to explain. Anyway, you solve them like this. For the first one, the first person can have any of 365 birthdays. So, 1/365. The second person can't have the same birthday, so there are only 364 possibilites. So, 1/364. The third person is 1/363, the fourth is 1/362, and the fifth is 1/361. To get the total, you multiply them all together. It's a huge number, 1/6302555018760. For the second problem, you'll get much smaller numbers. The first roll has 6 options, 1/6, the second roll has 5, 1/5, and the third roll has 4, 1/4. Multiply them together to get 1/120.