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Chapter 5: Q 5.43. (page 209)

Constract a venn diagram representing the event.

Part (a) A&B.

Part (b)A&B鈥�&C.

Short Answer

Expert verified

Part (a) A&B.

Part (b) A&鈥�B&C.

Step by step solution

01

Part (a) Step 1. Given information.

The following is the supplied statement:

Draw the venn diagram of A&B.

02

Part (a) Step 2.  The representation of (A & B).

To make a Venn diagram representing the shaded area of the region that is shared by AandB.

The shaded zone (blue colour) below represents the event, which is the common of AandB.

03

Part (b) Step 1.  Given information. 

The following is the supplied statement:

Draw the venn diagram A&B鈥�&C.

04

Part (b) Step 2.  The representation of A & B & C.

To make a Venn diagram representing the shaded area of the region that is shared by A,B&C

The shaded zone (Blue colour) below represents the event, which is the common ofA,B&C.

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Most popular questions from this chapter

World Series. The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919鈥�1921 World Series, when it was a best of nine). Thus it takes at least four games and no more than seven games to establish a winner. From the document World Series History on the Baseball Almanac website, as of November 2013, the lengths of the World Series are as given in the following table

Number of GamesFrequencyRelative Frequency
4210.200
5240.229
6240.229
7360.343

a. If X denotes the number of games that it takes to complete a World Series, identify the possible values of the random variable X.

b. Do the first and third columns of the table provide a probability distribution for X? Explain your answer.

c. Historically, what is the most likely number of games it takes to complete a series?

d. Historically, for a randomly chosen series, what is the probability that it ends in five games?

e. Historically, for a randomly chosen series, what is the probability that it ends in five or more games?

f. The data in the table exhibit a statistical oddity. If the two teams in a series are evenly matched and one team is ahead three games to two, either team has the same chance of winning game number six. Thus there should be about an equal number of six-and seven-game series. If the teams are not evenly matched, the series should tend to be shorter, ending in six or fewer games, not seven games. Can you explain why the series tend to last longer than expected?

Suppose that a simple random sample is taken from a finite population in which each member is classified as either having or not having a specified attribute. Fill in the following blanks.

(a) If sampling is with replacement, the probability distribution of the number of members sampled that have the specified attribute is a distribution.

(b) If sampling is without replacement, the probability distribution of the number of members sampled that have the specified attribute is a distribution.

(c) If sampling is without replacement and the sample size does not exceed % of the population size, the probability distribution of the number of members sampled that have the specified attribute can be approximated by a distribution.

Archery. An archer shoots an arrow into a square target 6 feet on a side whose center we call the origin. The outcome of this random experiment is the point in the target hit by the arrow. The archer scores 10 points if she hits the bull's eye-a disk of radius 1 foot centered at the origin; she scores 5 points if she hits the ring with inner radius 1 foot and outer radius 2 feet centered at the origin; and she scores 0 points otherwise. Assume that the archer will actually hit the target and is equally likely to hit any portion of the target. For one arrow shot, let S be the score.

(a) Obtain and interpret the probability distribution of the random variable S. (Hint: The area of a square is the square of its side length; the area of a disk is the square of its radius times.)

(b) Use the special addition rule and the probability distribution obtained in part (a) to determine and interpret the probability of each of the following events:

{S=5);{S>0};{S鈮�7);(5<S鈮�15);{S<15);and{S<0).

Age and senators. According to the congressional directory, the official directory of the U.S Congress prepared by the Joint Committee on printing the age distribution for senators in the U.S Congress as of fall 2013, is as shown in the following table.

Suppose that a U.S senator is selected at random. let

A = event the senator is under 50,

B = event the senator is in his or her 50s,

C = event the senator is in his or her 60s, and

S = event the senator is under 70.

Part (a) Use the table and the f/N rule to find P(S).

Part (b) Express event S in term of event A,B and C

Part (c) Determine P(A), P(B) and P(C).

Part(d) Compute P(S), Using the special addition rule and your answers from part (b) and part(c) Compare your answer with in parts (a)

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.
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