91Ó°ÊÓ

Constract a venn diagram representing the event.

Part (a) (A (not B)).

Part (b) ((A or B) & (not(A & B)))

What does it mean three events to be mutually exclusive.?

An experiment has 20 possible outcomes, all equally likely. An event can occur in five ways. The probability that the event occurs is .

Dice. When one die is rolled, the following six outcome are possible;

List the outcome constituting

A = event the die come up even

B = event the die come up 4 or more

C event the die come up at most 2, and

D= event the die come up 3.

Committee Selection. Refer to the image below for each of the following events, list the outcomes that constitute the event, and describe the event in words.

a. (not A)

b. (B&D)

c. (B or C)

A committee consists of five executives, three women and two men. Their names are Maria (M), John (J), Susan (S), Will (W), and Holly (H). The committee needs to select a chairperson and a secretary. It decides to make the selection randomly by drawing straws. The person getting the longest straw will be appointed chairperson, and the one getting the shortest straw will be appointed secretary. The possible outcomes can be represented in the following manner.

An experiment has 40 possible outcomes, all equally likely. An event can occur in 25 ways. The probability that the event is .

Diabetes Prevalence. In a report titled Behavioral Risk factor Surveillance System Summary Prevalence Report, the Centers for Distance control and Prevention Discuss the prevalence of diabetes in the Unites states. The following table provides a diabetes prevalence frequency distribution for the 50 U.S state based on the question "Hhave you ever been told by a doctor that you have diabetes?"

For a randomly selected, let

A = event that the state has a diabetes prevalence percentage of at least 8%

B = event that the state has a diabetes prevalence percentage of less than 7%

C= event that the state has a diabetes prevalence percentage of at least 6% but less than 13%

D = event that the state has a diabetes prevalence percentage of less than 9%

Describe each of the following event in words and determine the number of outcomes (states) that constitute each event.

Part (a) (not C)

Part (b) (A & B)

Part (c) (C or D)

Part (d) (C & B)

Dice. Refer to exercise 5.53.

a Are events A and B mutually exclusive?

b Are events B and C mutually exclusive?

c Are events A, C and D mutually exclusive?

d Are there three mutually exclusive events among A, B, C and D? four?

Die and coin. Consider the following random experiment : First , roll a die and observe the number of dots facing up: then toss a coin the number of times that the die shows and observe the total number of heads. Thus , if the die shows three dots facing up and the coin (which is then tossed tree times) comes up heads exactly twice, then the outcome of the experiment can be represent as (3,2).

Part (a) Determine a sample space for this experiment.

Part (b) Determine the events that the total number of heads is even.

Jurors. From 10 men and 8 women in a pool of potential jurors 12 are chosen at random to constitute a jury. Suppose that you observe the number of men who are chosen for the jury. Let A be the event that at least half of the 12 jurors are men, and let B be the event that at least half of the 8 women are on the jury.

Part (a) Determine the sample space for this experiment

Part (b) Find (A or B) ,(A & B) and (A &(not B)), listing all the outcomes for each of those three events

Part (c) Are events A and B are mutually exclusive.? are events A and (not B)? are events (not A) and (not B)? Explain.