## Estimating Chances

Problems and tasks from a variety of sources intended to illustrate the way mathematics arises in life and work.

Chance of Rain. The weather report on Friday night indicates that the chance of rain on Saturday is 50%, as it is also on Sunday. What is the probability that there will be rain on at least one of the two weekend days? Would it be safe to plan an outdoor event?

Winning the Lottery. You have just won a lottery providing \$20,000 per year for the next ten years. Realizing that it will be a great shock to lose this annual award when the ten years are up, you decide to invest part of each year's award so that by drawing on this investment you can continue to spend for a total of fifty years at the same rate that you spend during the first ten. How much should you invest each year to make this possible? How much more could you spend every year if you delay spending anything for the first two years--and just invest the entire \$20,000 in each of those years?

Coincidences. Which is more likely--that two students in a class have the same birthday, or the same first and last initials?

Rounding Off. Whenever numbers are rounded off, their sums may not agree with the rounded sum of the original numbers. Computer spreadsheets that hold numbers accurately but display rounded values will often produce totals that appear inaccurate. Thus if 1.4 and 1.3 are rounded before adding, the result is 1+1 = 2, whereas if they are added and then rounded, the result is 2.7, which rounds to 3. What is the probability, under these conditions, that 1+1 = 2?