Chapter 5: Probability and Random Variables

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.

Horse Racing. In a horse race, the odds against winning are as shown in the following table. For example, the odds against winning are 8 to 1 for horse #1.

List the outcomes constituting.

A = event on e of the top two favorites wins (the top two favorites are the two horse with the lowest odds against winning).

B = events the winning horse's number is above 5.

C = events the winning horse's number is at most 3,that is 3 or less and

D = event on e of the two long shots wins (the top long shots are the two horse with the highest odds against winning).

Committee selection. A committee consists of five executives three woman and two men. Their names are maria (M), John (J), Susan (S) Will (W), 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 outcome can be represented in the following manner.

Here. for example. MS represent the outcome that maria is appointed chairperson and Susan is appointed secretary. List the outcome constituting each of the following four events.

A = event a male is appointed chairperson.

B = event Holly is appointed chairperson.

C = event Will is appointed Secretary.

D = event only female are appointed.

Coin Tossing. When a dime is tossed four times , there are the following 16 possible outcomes.

Here, for example, HTTH represents the outcomes that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes constituting each of the following four events.

A = event exactly two heads are tossed,

B = event the first two tosses are tails,

C = event the first toss is heads,

D = event all four tosses come up the same.

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

1. (not A)
2. (A & B )
3. (B or C)

When one die is rolled, following outcomes are possible :

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

1. (not C)
2. (C & D)
3. (A or C)

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.

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

a. (not B) b. (A & B) c. (C or D)

Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes constituting each of the following four events.

A = event exactly two heads are tossed,

B = event the first two tosses are tails,

C = event the first toss is heads,

D= event all four tosses come up the same.

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)