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 20 years and over at random. Define two events: A = A= the person chosen is obese B = B= the person chosen is overweight, but not obese

Answer 1

Answer:

Part a: The two events are termed as disjoint because the event B clearly rules out the obese person

Part b: In the plain language, the event "A or B" means that the person is  overweight or obese. Its probability is 0.74.

Part c: If C is the event that the person chosen has normal weight or less, its probability is 0.26.

Step-by-step explanation:

As per the question obtained from the google search, the question has 3 parts as follows:

Part a

Explain why events A and B are disjoint.

Solution

The two events are termed as disjoint because the event B clearly rules out the obese person so the events are disjoint. so the correct option as given in the complete question is A.

Part b

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

What is P(A or B)? (Enter your answer to two decimal places.)

Solution

In the plain language, the event "A or B" means that the person is  overweight or obese. The correction option as given in the complete question is a.

P(A or B) is given as

P(A or B)=P(AUB)=P(A)+P(B)-P(A∩B)

Here from the data of

P(A)=0.41

P(B)=0.33

P(A∩B)=0 (As the events are disjoint)

P(A or B)=P(AUB)=0.41+0.33-0

P(AUB)=0.74

So the probability of A or B is 0.74.

Part c

If C is the event that the person chosen has normal weight or less, what is

P(C)? (Enter your answer to two decimal places.)

Solution

P(C) is given as

P(C)=1-P(AUB)

P(C)=1-0.74

P(C)=0.26

So the probability of event C is 0.26.