1. What computation would you do to figure out for a group of 8 people what the probability is that two people have the same birthday? (just write out the mulitplication, don't crunch the numbers)(assume 366 equally likely days per year)

1 - (366/366)*(365/366)*(364/366)*(363/366)*(362/366)*(361/366)*(360/366)*(359/366)

2. In a group of 8 people, what is the probability that two people's birthdays are in the same month?

P(all different) = (12/12)(11/12)(10/12)(9/12)(8/12)(7/12)(6/12)(5/12) = .05

P(all different) = 5%

1 - (12/12)(11/12)(10/12)(9/12)(8/12)(7/12)(6/12)(5/12) = .95

P(2 in the same month) = 95%

3. If everyone in a group of 4 people rolls a 6 sided die, what is the probability that (at least) two people roll the same number?

P(all different) = (6/6)*(5/6)*(4/6)*(3/6) = .28

P(all different) = 28%

1 - (6/6)*(5/6)*(4/6)*(3/6)= .72

P(2 the same number)= 72%

4. If everyone in a group of 5 people rolls a 20 sided die, what is the probability that (at least) two people roll the same number?

P(all different) = (20/20)*(19/20)*(18/20)*(17/20)*(16/20) = .58

1 -(20/20)* (19/20)*(18/20)*(17/20)*(16/20) = .42

P(2 the same) = 42%

5. If I roll 3 8-sided dice, what is the probability that (at least) two of the dice will have roll same number?

P(all different) = (8/8)(7/8)(6/8) = .66

1 - (7/8)(6/8)

P(2 the same) = 34%