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Words 586

Pages 3

Part I

Define the 4 rules of probability.

1. Any probability is a number between 0 and 1

a. P(A) satisfies 0 ≤ P(A) ≤ 1

2. All positive outcomes together must have probability 1

a. P(S) = 1

3. If 2 events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities

a. P(A or B) = P(A) + P(B)

4. The probability that an event does not occur is 1 minus the probability that the event does not occur

a. P(A does not occur) = 1 – P(A)

Part II

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 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) = 0.32 and P(B) = 0.34.

(a) Explain why events A and B are disjoint.

Event B rules out any subject that is obese, so there is no type of overlap with event A

(b) Say in plain language what the event “A or B” is. What is P(A or B)?

“A or B” is the event “The person chosen is obese”

P(A or B) = P(A) + P(B) = 0.32 + 0.34 = 0.66

(c) If C is the event that the person chosen has normal weight or less, what is P(C)?

P(C) = 1.00 – 0.66 = 0.34

Part III

Choose a person aged 19 to 25 years at random and ask, “In the past seven days, how many times did you go to an exercise or fitness center or work out?” Call the response X for short. Based on a large sample survey, here is a probability model for the answer you will get:4

(a) Verify that this is a legitimate discrete probability model.

All eight probabilities above when added together are equal to 1

(b) Describe the event X < 7 in words. What is P(X < 7)?

“X < 7” means the individual did not work out every day in the…...

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