Ch 11 test practice

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Solve the problem by applying the Fundamental Counting Principle with two groups of items.1) A person can order a new car with a choice of 12 possible colors, with or without air

conditioning, with or without heated seats, with or without anti-lock brakes, with orwithout power windows, and with or without a CD player. In how many different wayscan a new car be ordered in terms of these options?

1)

Evaluate the factorial expression.

2) 500!499!

2)

Use the formula for nPr to evaluate the expression.

3) 10P3 3)

Solve the problem.4) In how many distinct ways can the letters in MANAGEMENT be arranged? 4)

In the following exercises, does the problem involve permutations or combinations? Explain your answer. It is notnecessary to solve the problem.

5) Five of a sample of 100 computers will be selected and tested. How many ways are thereto make this selection?

5)

Use the formula for nCr to evaluate the expression.

6) 10C9 6)

7) To win at LOTTO in a certain state, one must correctly select 6 numbers from a collectionof 53 numbers ( one through 53.) The order in which the selections is made does notmatter. How many different selections are possible?

7)

Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowestterms.

8) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. If the pointer lands on a borderline, spin again.

Find the probability that the arrow will land on 1 or 5.

8)

9) You are dealt one card from a standard 52-card deck. Find the probability of being dealt apicture card.

9)

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10) This problem deals with eye color, an inherited trait. For purposes of this problem, assumethat only two eye colors are possible, brown and blue. We use b to represent a blue eyegene and B a brown eye gene. If any B genes are present, the person will have brown eyes.The table shows the four possibilities for the children of two Bb (brown-eyed) parents,where each parent has one of each eye color gene.

Second ParentB b

First Parent B BB Bbb Bb bb

Find the probability that these parents give birth to a child who has blue eyes.

10)

Use the empirical probability formula to solve the exercise. Express the answer as a fraction. Then express theprobability as a decimal, rounded to the nearest thousandth, if necessary.

11) The table below represents a random sample of the number of deaths per 100 cases for acertain illness over time. If a person infected with this illness is randomly selected from allinfected people, find the probability that the person lives 3-4 years after diagnosis.Years after Diagnosis Number deaths1-2 153-4 355-6 167-8 99-10 611-12 413-14 215+ 13

11)

Solve the problem.12) A group consists of 6 men and 5 women. Four people are selected to attend a conference.

In how many ways can 4 people be selected from this group of 11? In how many ways can4 men be selected from the 6 men? Find the probability that the selected group will consistof all men.

12)

13) A committee consisting of 6 people is to be selected from eight parents and four teachers.Find the probability of selecting three parents and three teachers.

13)

You are dealt one card from a 52-card deck. Find the probability that you are not dealt:14) a 3. 14)

In 5-card poker, played with a standard 52-card deck, 52C5, or 2,598,960 different hands are possible. The probabilityof being dealt various hands is the number of different ways they can occur divided by 2,598,960. Find the probabilityof not being dealt this type of hand.

15) Four of a kind: 4 cards with the same number, plus 1 additional card, if the number of

ways this hand can occur is 624, and the probability of this hand is 6242,598,960

15)

You are dealt one card from a 52-card deck. Find the probability that you are dealt:16) a numbered card or a heart 16)

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Solve the problem.17) The biology faculty at a college consists of 5 professors, 12 associate professors, 11 assistant

professors, and 6 instructors. If one faculty member is randomly selected, find theprobability of choosing a professor or an instructor.

17)

Solve the problem involving probabilities with independent events.18) A spinner is used for which it is equally probable that the pointer will land on any one of

six regions. Three of the regions are colored red, two are colored green, and one is coloredyellow. If the pointer is spun once, find the probability it will land on green and thenyellow.

18)

Solve the problem that involves probabilities with events that are not mutually exclusive.19) Consider a political discussion group consisting of 3 Democrats, 4 Republicans, and 8

Independents. Suppose that two group members are randomly selected, in succession, toattend a political convention. Find the probability of selecting an Independent and then aDemocrat.

19)

Numbered disks are placed in a box and one disk is selected at random.20) If there are 4 red disks numbered 1 through 4, and 8 yellow disks numbered 5 through 12,

find the probability of selecting a disk numbered 3, given that a red disk is selected.20)

The table shows the number of employed and unemployed workers in the U.S., in thousands, in 2000.

Employed UnemployedMale 67,761 2433Female 58,655 2285

Assume that one person will be randomly selected from the group described in the table.21) Find the probability of selecting a person who is employed, given that the person is male. 21)

The table shows claims and their probabilities for an insurance company.

Amount of Claim Probability$0 0.60$50,000 0.25$100,000 0.09$150,000 0.04$200,000 0.01$250,000 0.01

22) (a) Calculate the expected value.(b) How much should the company charge as an average premium so that it breaks evenon its claim costs?(c) How much should the company charge to make a profit of $110 per policy?

22)

Solve the problem that involves computing expected values in a game of chance.23) A numbers game run by many state governments allows a player to select a three-digit

number from 000 to 999. There are 1000 such numbers. A bet of $9 is placed on anumber. If the number is selected, the player wins $900. If any other number is selected,the player wins nothing. Find the expected value for the game.

23)

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Answer KeyTestname: CH 11

1) 3842) 5003) 7204) 226,8005) Combinations, because the order of the computers selected does not matter.6) 107) 22,957,480

8) 25

9) 313

10) 14

11) 35100

; 0.35

12) 330; 15; 122

13) 833

14) 1213

15) 2,598,3362,598,960

16) 1013

17) 1134

18) 118

19) 435

20) 14

21) 67,76170,194

22) (a) $32,000 (b) $32,000 (c) 32,11023) -$8.10

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