STAT 301 - Business Statistics
Class Activity - Probability Review

Work together with your fellow group members to answer the following probability problems. (Each of you should be writing down solutions to these problems for your notes.) We will periodically pause your work to go over solutions to these problems.

1) Four people are chosen at random. What is the probability that their birthdays are all in the same month? The chance that they are all in different months? The chance that at least two are in the same month?

2) Academic-types tend to think a 90% success rate is wonderful. ("That’s an A!") But there are plenty of other situations where 90% is nowhere good enough. (Next time you step on the elevator in LBC, do you want there to be only a 90% chance of safely reaching your floor?) In this problem we will look at just how reliable things need to be, in practice. In particular, we’ll look at the chance of getting through a year without a commercial aircraft accident.

a) Begin by doing a little bit of research: Just how many commercial passenger flights are there in the world, each year? (For now let’s leave aside such things as private planes, cargo jets, and military flights.) Hint: there is this wonderful new-fangled invention called the "internet" that you might use to get a handle on this number.

b) Suppose each flight (from Part A) has a 99% chance of reaching its destination safely. What is the probability that there is at least one airline crash in the coming year?

c) What if the chance of a safe flight is 99.9%. Now what’s the probability of at least one air crash in the coming year?

d) How safe do we need to make each individual flight, to get the overall chance of at least one crash in the coming year to be below 0.1%?

3) There are two major "big prize" lotteries in the U.S. — Mega Millions and Powerball. In this problem, we’ll look at the chance of winning the Mega Millions lottery. According to the Oracle Of All Knowledge (i.e., Wikipedia), "the current version of Mega Millions requires players to match 5 of 70 white balls, and the gold-colored ‘MegaBall’ from a second field, of 25 numbers."

a) If you buy one Mega Millions ticket, what is your probability of winning?

b) If fifty million tickets are sold, what the probability that at least one of them is a winner?

c) For the last big jackpot, a total of 352,227,744 tickets were sold. For that many tickets sold, what’s the probability that there would be no winner (and the jackpot would roll over to another drawing)?