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Chapter 3: Q. 108 (page 227)

The events "Other" and "Up for reelection in November 2016" are

a. mutually exclusive.

b. independent.

c. both mutually exclusive and independent.

d. neither mutually exclusive nor independent.

Short Answer

Expert verified

The events Other and Up for reelection in November 2016 are mutually exclusive.

Step by step solution

01

Step1:Calculate  other and up for reelection(part a)

Events A and B are mutually exclusive if the probability of both events A and B is the same.

calculating the likelihood of event Other and is up for reelection in 2016:

P=067=0

02

Step2:Find A and B are mutually exclusive(part b)

Events A and B cannot be independent if they are mutually exclusive. That's because they can't happen at the same time if they're mutually exclusive. If we know that B occurred, we can be certain that A did not. Thus:

P(A鈭�B)=0鈮�P(A)

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Most popular questions from this chapter

An experiment consists of first rolling a die and then tossing a coin.

a. List the sample space.

b. Let A be the event that either a three or a four is rolled first, followed by landing a head on the coin toss. Find PA.

c. Let B be the event that the first and second tosses land on heads. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification.

You have a fair, well-shuffled deck of 52 cards. It consists of four suits. The suits are clubs, diamonds, hearts, and spades. There are 13 cards in each suit consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), and K (king) of that suit. S = spades, H = Hearts, D = Diamonds, C = Clubs. Suppose that you sample four cards without replacement.

Which of the following outcomes are possible? Answer the same question for sampling with replacement.

a. QS, 1D, 1C, QD

b. KH, 7D, 6D, KH

c. QS, 7D, 6D, KS

Explain what is wrong with the following statements. Use complete sentences.

a. If there is a 60%chance of rain on Saturday and chance of rain on Sunday, then there is a 130%chance of rain over the weekend.

b. The probability that a baseball player hits a home run is greater than the probability that he gets a successful hit.

In a standard deck, there are 52cards. Twelve cards are face cards (F) and 40cards are not face cards (N). Draw two cards, one at a time, without replacement. The tree diagram is labeled with all possible probabilities.

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b. Find P(NF).

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Hint: "At most one face card" means zero or one face card.

d. Find P (at least on face card).

Hint: "At least one face card" means one or two face cards.

Use the following information to answer the next two exercises. You see a game at a local fair. You have to throw a dart at a color wheel. Each section on the color wheel is equal in area.

Let B = the event of landing on blue.

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If you land on red, you don鈥檛 get a prize. What is P(R)?
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