24SP MATH 101 Mathematics for Liberal Arts (05),

Homework Week 4

1.

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JMODD6 3.4.01.

A group of 30 is selected at random. What is the probability that at least two of them will have the same birthday? (Round the answer to four decimal places.) __________________

2

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In 1990, California switched from a 6/49 lottery to a 6/53 lottery. Later, the state switched again to a 6/51 lottery.

(a) Find the probability of winning first prize in a 6/49 lottery. __________ (b) Find the probability of winning first prize in a 6/53 lottery. ______________

(c) Find the probability of winning first prize in a 6/51 lottery.

_________________ (d) How much more probable is it that one will win the 6/49 lottery than the 6/53 lottery? (Round your answer to the nearest whole number.) __________________ %

3.

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JMODD6 3.4.18.

Do the following. (Round the answers to six decimal places.)

1. Find the probability of being dealt a "queensoverjacks" full house (threequeensand twojacks). ____________ (b) Find the probability of being dealt a full house. ________________

4.

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JMODD6 3.4.19COMBO.

You order twelve burritos to go from a Mexican restaurant, five with hot peppers and seven without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability thatnone of them have hot peppers. (Round the answer to three decimal places.) ____________________

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JMODD6 3.4.28.

Threehundred people apply for three jobs.90of the applicants are women.

(a) If three persons are selected at random, what is the probability that all are women? (Round the answer to six decimal places.) ________________________ (b) If three persons are selected at random, what is the probability that two are women? (Round the answer to six decimal places.)

_________________ (c) If three persons are selected at random, what is the probability that one is a woman? (Round the answer to six decimal places.) _________________ (d) If three persons are selected at random, what is the probability that none is a woman? (Round the answer to six decimal places.) __________________ (e) If you were an applicant, and the three selected people were not of your gender, should the above probabilities have an impact on your situation? Why?

__________Yes, the probabilities indicate the presence of gender discrimination.

___________No, because in the hiring process, all outcomes are not equally likely.

6.

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JMODD6 3.5.14.

On the basis of his sale records, a salesman knows that his weekly commissions have the following probabilities. Find the salesman's expected commission. $ ____________________

Commission	0	$1000	$2000	$3000	$4000
Probability	0.11	0.2	0.49	0.1	0.1

7.

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JMODD6 3.5.20.

You are on a TV show. You have been asked to either play a dice game five times or accept a $50 bill. The dice game works like this.

If you roll a 1, 2 or 3, you win$50. If you roll a 4 or 5, you lose$20. If you roll a 6, you lose$88.

Should you play the game? Use expected values and decision theory to justify your answer. (Round the answer to the nearest cent.)

Yes

No

EV= $ __________

8.

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JMODD6 3.5.26.

Debra is buying prizes for a game at her school's fundraiser. The game has three levels of prizes, and she has already bought the second and third prizes. She wants the first prize to be nice enough to attract people to the game. The game's manufacturer has supplied her with the probabilities of winning first, second, and third prizes. Tickets cost $3 each, and she wants the school to profit an average of $1 per ticket. How much should she spend on each first prize? (Give your answer to the nearest cent.)

Prize	Cost of prize	Probability
1st	$	0.15
2nd	$1.19	0.30
3rd	$0.77	0.45

9.

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JMODD6 3.6.01.

LetHbe the event that a job candidate is hired, and letQbe the event that a job candidate is well qualified. Use the symbolsH,Q, |, andto write the probability that a job candidate is hiredandthat the candidate is well qualified.

p(H|Q)

p(HQ)

p(Q|H)

p(QH)

p(QH)

10.

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JMODD6 3.6.09DEF.

In a newspaper poll concerning violence on television,600people were asked, "What is your opinion of the amount of violence on prime-time television--is there too much violence on television?" Use the data in the table below to find the given probabilities. Also, complete the following sentences explaining what each means. (Round the percentages to one decimal place.)

	Yes	No	Don't Know	Total
Men	162	85	23	270
Women	256	55	19	330
Total	418	140	42	600

(a)p(W|N) =_______________ About____________% of

a. those who said no were women

b. the women said no

c. the respondents said no and were women

d. those surveyed said no

e. those surveyed were women. (b)p(NW) =___________ About_____________% of---Select---

a. those who said no were women

b. the women said no

c.the respondents said no and were women

d. those surveyed said no

e. those surveyed were women. (c)p(WN) =______________ About______________% of---Select---

a. those who said no were women

b. the women said no

c. the respondents were women and said no

d. those surveyed said no

e. those surveyed were women.

11.

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JMODD6 3.6.16.

Cards are dealt from a full deck of 52. Find the probabilities of the given events.

(a) The first card is a king. ______________ (b) The second card is a king, given that the first was a king. ____________ (c) The first and second cards are both kings. _____________ (d) Draw a tree diagram illustrating this. (Do this on paper. Your instructor may ask you to turn in this diagram. Your diagram need not be a complete tree. It should have all the branches referred to in parts (a), (b), and (c), but it does not need other branches.)

12.

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JMODD6 3.6.21BC.

A single die is rolled. Find the probabilities of the given events.

(a) Rolling a6, given that the number rolled is even. ____________ (b) Rolling a6, given that the number rolled is odd. ____________

13.

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JMODD6 3.6.25.

A pair of dice is rolled. Find the probabilities of the given events.

(a) The sum is4. _____________ (b) The sum is4, given that the sum is less than6. ______________ (c) The sum is less than6, given that the sum is4. ____________

14.

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JMODD6 3.6.29.

To determine what effect the salespeople had on purchases, a department store polled 700 shoppers as to whether or not they had made a purchase and whether or not they were pleased with the service. Of those who had made a purchase, 125 were happy with the service and 111 were not. Of those who had made no purchase, 148 were happy with the service and 316 were not. Find the probability that a shopper who was happy with the service had made a purchase (round the answer to the nearest hundredth). ________________ What can you conclude? About______________% of those who were happy with the service made a purchase.

15.

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JMODD6 3.6.41COMBO.

A personal computer manufacturer buys38%of its chips from Japan and the rest from the United States.1.7%of the Japanese chips are defective, and1.1%of the American chips are defective. Find the probability that a chip is defective and made inthe United States. (Round the answer to five decimal places.) _________________

16.

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JMODD6 3.6.47AB.

Data on the governors of the fifty states are given in the table.

	Democrats	Republicans	Independents
Male	12	28	0
Female	8	2	0

(a) Find the probability that a governor is female, given that the governor is a Democrat.____________________ (b) Find the probability that a governor is female, given that the governor is a Republican. __________________ 17.

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JMODD6 3.6.58.

The University of Metropolis requires its students to pass an examination in college-level mathematics before they can graduate. The students are given three chances to pass the exam; 61% pass it on their first attempt, 63% of those that take it a second time pass it then, and 42% of those that take it a third time pass it then. What percent of the students are not allowed to graduate because of their performance on the exam? (Round the answer to the nearest whole number.) ______________________%

18.

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JMODD6 3.6.64.

In a newspaper poll concerning violence on television, 600 people were asked, "What is your opinion of the amount of violence on prime-time television-is there too much violence on television?" Use the data in the table to find the following probabilities, whereYis the event "saying yes," andMis the event "being a man." (Round the answers to two decimal places.)

	Yes	No	Don't Know	Total
Men	162	95	23	280
Women	256	45	19	320
Total	418	140	42	600

(a)p(Y'|M) =___________ (b)p(Y|M') =___________ (c)p(Y'|M') =___________ (d) Which event is the complement of the eventY|M?

Y'|M

'Y'|M

Y|M'

19.

[-/1 Points]DETAILS

JMODD6 3.4.07.

Find the probability of winning second prize (that is, picking five of the six winning numbers) with a 6/44 lottery, as played in Connecticut, Missouri, Oregon, and Virginia. (Round the answer to five decimal places.)____________________

20.

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JMODD6 3.4.21COMBO.

You order twelve burritos to go from a Mexican restaurant, five with hot peppers and seven without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability thatexactly one has hot peppers. (Round the answer to three decimal places.)________________

21.

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JMODD6 3.4.25COMBO.

You order twelve burritos to go from a Mexican restaurant, five with hot peppers and seven without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability thatat most two have hot peppers. (Round the answer to three decimal places.) __________________

22

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JMODD6 3.5.11.

Determine a casino's expected net income from a 24-hour period at a single roulette table if the casino's total overhead for the table is $50 per hour and if customers place a total of $7,000 on single-number bets, $4,000 on two-number bets, $4,000 on four-number bets, $3,000 on six-number bets, $7,000 on low-number bets, and $8,000 on red-number bets. (Assume the expected value of each of these $1 bets in roulette is -$0.053.) $___________________________

23.

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JMODD6 3.5.34.

Mr. and Mrs. Trump have applied to the Trustworthy Insurance Co. for insurance on Mrs. Trump's diamond tiara. The tiara is valued at$96,000. Trustworthy estimates that the jewelry has a2.5%chance of being stolen in any one year. Use expected values to determine the annual insurance premiump. p $______________________