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Chapter 3: Q. 108 (page 227)

Use the information in the Table3.19to answer the next eight exercises. The table shows the political party affiliation of each of localid="1649516803996" 67members of the US Senate In June localid="1649516807155" 2012. and when they are up freelection.

The events "Other" and "Up for reelection in November localid="1649516811372" 2016' are

a. mutually exclusive.

b. independent.

c. both mutually exclusive and independent.

d. neither mutually exclusive nor independent

Short Answer

Expert verified

In November 2016, the events Other and Up for reelection are mutually exclusive.

As a result, mutually exclusive is the correct answer.

Step by step solution

01

Given

The table shows the political party affiliation of each of 67members of the US Senate In June 2012. and when they are up reelection.

02

Finding the probability of event Other and Is up for reelection in 2016

The total as:

Events A and B are mutually exclusive if the probability of event AAND Bequals 0.

Finding the probability of event Other and Is up for reelection in 2016:

P=067=0

Thus, we can conclude that events are mutually exclusive.

If events A and B are mutually exclusive, then they cannot be independent. That is because, if they are mutually exclusive, they cannot happen at the same time. If we know that B happened, then we immediately know that A didn't. Thus:

P(A鈭�B)=0鈮�P(A)

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Most popular questions from this chapter

Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1,2,3,4and5. The three yellow cards are numbered 1,2,and3. The cards are well shuffled. You randomly draw one card.

鈥� G = card drawn is green

鈥� E = card drawn is even-numbered

a. List the sample space.

b. P(G)=_____

c. P(G|E)=_____

d. P(GANDE)=_____

e. P(GORE)=_____

f. Are G and E mutually exclusive? Justify your answer numerically

Use the information in the Table 3.19to answer the next eight exercises. The table shows the political party affiliation of each of 67members of the US Senate In June 2012. and when they are up freelection.

Suppose that a member of the US Senate is randomly selected. what is the probability that the senator Is up for reelection in November 2014, knowing that this senator is a Republican?

When the Euro coin was introduced in 2002, two math professors had their statistics students test whether the Belgian one Euro coin was a fair coin. They spun the coin rather than tossing it and found that out of 250spins,140showed a head (event H) while 110showed a tail (event T). On that basis, they claimed that it is not a fair coin.

a. Based on the given data, find P(H) and P(T).

b. Use a tree to find the probabilities of each possible outcome for the experiment of tossing the coin twice.

c. Use the tree to find the probability of obtaining exactly one head in two tosses of the coin.

d. Use the tree to find the probability of obtaining at least one head

Use the following information to answer the next two exercises. The following are real data from Santa Clara County, CA. As of a certain time, there had been a total of 3,059documented cases of AIDS in the county. They were grouped into the following categories:

Suppose a person with AIDS in Santa Clara County is randomly selected.

a. Find P(Person is female).

b. Find P(Person has a risk factor heterosexual contact).

c. Find P(Person is female OR has a risk factor of IV drug user).

d. Find P(Person is female AND has a risk factor of homosexual/bisexual).

e. Find P(Person is male AND has a risk factor of IV drug user).

f. Find P(Person is female GIVEN person got the disease from heterosexual contact).

g. Construct a Venn diagram. Make one group females and the other group heterosexual contact

A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.40, P(D) = 0.30 and P(D|B) = 0.5.

a. Find P(B鈥�).

b. Find P(D AND B).

c. Find P(B|D).

d. Find P(D AND B鈥�).

e. Find P(D|B鈥�).
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