Although the rules of probability are just basic facts about percents or proportions, we need to be able to use the language of events and their probabilities. Choose an American adult aged 20 years and over at random. Define two events: A= the person chosen is obese
B= the person chosen is overweight, but not obese.

According to the National Center for Health Statistics,
P(A)=0.38
P(B)=0.33

1. Explain why events A and B are disjoint.

a. Because event B rules out obese subjects.
b. Because an obese person is certainly overweight.
c. Because some people may be considered obese and overweight.
d. Because some people are not obese nor overweight.

2. Say in plain language what the event "A or B" is.

a. "A or B" is the event that the person chosen is overweight or obese.
b. "A or B" is the event that the person chosen is overweight and obese.
c. "A or B" is the event that the person chosen is overweight or obese or both.
d. "A or B" is the event that the person chosen is not obese or not over weight.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.