Question

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.

Answer 1

a. Because event B rules out obese subjects.

b. "A or B" is the event that the person chosen is overweight and obese.

Explanation:

1. Disjoint events are those events which do not have the same elements. Event A and event B can only be disjoint if they both have separate subjects that is event A contains obese persons and event B contains overweight persons.

Therefore they are only disjoint when set B rules out ( leaves out) obese people. So choice a is the best answer.

Disjoint events are also called mutually exclusive events

2. In statistics the symbol or means including. Event A or B would mean including both types of person obese and overweight. In mathematical expression it is written as

P (A or B) = P (A) + P (B) For mutually exclusive events. ( disjoint events)