in the fileHomework 11

July 20, 2016

MATH 106-C01 – Quantitative Reasoning

Due date: July 21, 2016, at 10:30am

Exercise 1. Do problems 6, 8, 10, 18 and 24 from p586-587 of the textbook. Show your

work.

Exercise 2. Do problem 40 from p587 of the textbook.

Exercise 3. (extra credit) Do problem 52 from p587 of the textbook. Show your work.

Exercise 4. Do the following problems. Show your work.

1. Suppose you are drawing two cards from the standard deck, without replacement.

What is the probability of rolling two dice, and getting the same number? Show your

work.

2. What is the probability of flipping a coin 3 times and getting the same outcome each

time? Show your work.

Exercise 5. Do problems 10, 14, 22, 24 and 34 ( you will have to do problem 19 for part b,

but the answer is in the back of the book) from p594-595 of the textbook. Show your work.

1

C, D, E}. If they ct

odds against each

(a) Cathy

(c) a person whose

Solve each probability problem.

5. Using Spinners to Generate Numbers Suppose the spin-

ner shown here is spun once, to determine a single-digit

number, and we are interested in the event E that the

resulting number is odd. Give each of the following.

11

of

st

2

11. Random Selection a

hit singles from the

ley Lewis, two by

four by The Coast

randomly selects

the probability it

(a) Smiley Lewis

(c) Bobby Darin

(e) Fats Domino

1

3

(a) the sample space

(b) the number of favorable

outcomes

(c) the number of unfavor-

able outcomes

(d) the total number of possi-

ble outcomes

(e) the probability of an odd number

(f) the odds in favor of an odd number

Lining Up Preschool children Kim Lenaghan’s group

of preschool children includes nine girls and seven boys.

If Kim randomly selects one child to be first in line, with

E being the event that the one selected is a girl, give

each of the following.

(a) the total number of possible outcomes

(b) the number of favorable outcomes

(c) the number of unfavorable outcomes

(d) the probability of event E

(e) the odds in favor of event E

12. Probabilities in Co

(a) Write out the

Determine the p

(b) no heads

(d) exactly two

13. Number Sums for

rolling of two fair

Reproduce that

likely ordered p

two dice). Then

(a) 2

7.

(d) 5

(g) 8

(j) 11

7. Using Spinners to Generate Numbers The spinner of

Exercise 5 is spun twice in succession to determine a

two-digit number. Give each of the following.

(a) the sample space

(b) the probability of an odd number

(c) the probability of a number with repeated digits

(d) the probability of a number greater than 30

(e) the probability of a prime number

ty

In Exercises 14 ano

14. Probability of Sa

project, 200 sec

nated. Find the

seed of this tyr

@

8) Probabilities in Coin Tossing Two fair coins are tossed

(say a dime and a quarter). Give each of the following.

11.1

Basic Concepts lll 585

the spinner shown

(a) the sample space

(b) the probability of heads on the dime

(c) the probability of heads on the quarter

(d) the probability of getting both heads

(e) the probability of getting the same outcome on

both coins

9. Drawing Balls from an Urn Anne Kelly

randomly chooses a single ball from

the urn shown here. Find the odds

against each event.

(a) red

(b) yellow (c) blue

10) Random Selection of Club Officers Five people (Alan, Bill,

Cathy, David, and Evelyn) form a club N = {A, B,

C, D, E}. If they choose a president randomly, find the

odds against each result.

(a) Cathy

(b) a woman

(c) a person whose name begins with a consonant

ppose the spin-

ne a single-digit

event E that the

he following

11. Random Selection of Fifties Music Butch LeBeau has fifty

hit singles from the fifties, including exactly one by Smi-

ley Lewis, two by The Drifters, three by Bobby Darin,

four by The Coasters, and five by Fats Domino. If Butch

randomly selects one hit from his collection of fifty, find

the probability it will be by each of the following.

(a) Smiley Lewis (b) The Drifters

(c) Bobby Darin

(d) The Coasters

(e) Fats Domino

2

1

3

12. Probabilities in Coin Tossing Three fair coins are tossed.

omnle snace.

selected location in California will be forested.

two

24.

25.

16. Probabilities of Two Daughters Among Four Children In

Example 3, what would be Kathy’s probability of hay-

ing exactly two daughters if she were to have four chil-

dren altogether? (You may want to use a tree diagram

to construct the sample space.)

17. Rolling Altered Dice A six-sided die has been altered so

that the side that had been a single dot is now a blank

face. Another die has a blank face instead of the face

with four dots. What is the probability that a sum of 7 is

rolled when the two dice are thrown? (Mathematics

Teacher calendar problem)

26.

18 Probability of Location in a Tunnel Mr. Davis is driving

through a tunnel that is eight miles long. At this instant,

what is the probability that he is at least six miles from

one end of the tunnel? (Mathematics Teacher calendar

problem)

Sup

car

Tal

ing

27.

28.

29.

Genetics in Snapdragons Mendel found no dominance in

snapdragons (in contrast to peas) with respect to red and

white flower color. When pure red and pure white parents are

crossed (see Table 2), the resulting Rr combination (one of

each gene) produces second-generation offspring with pink

flowers. These second-generation pinks, however, still carry

one red and one white gene, so when they are crossed the

third generation is still governed by Table 3.

Find each probability for third-generation snapdragons.

19. P(red) 20. P(pink)

21. P(white)

Suj

and

the

30.

31.

32.

Genetics in Pea Plants

Mendel also investigated various

characteristics besides flower color. For example, round peas

are dominant over recessive wrinkled peas. First, second,

and third generations can again be analyzed using Tables 2

and? whara Pranmoranti round and

Ger

again be analyzed using Tables 2

and 3, where R represents round and r represents wrinkled.

22. Explain why crossing pure round and pure wrinkled

first-generation parents will always produce round peas

in the second-generation offspring.

7

d

m

T

23. When second-generation round pea plants (each of

which carries both R and r genes) are crossed, find the

probability that a third-generation offspring will have

(a) round peas,

(b) wrinkled peas.

er

of

33.

Genetics of Cystic Fibrosis Cystic fibrosis is one of the most

common inherited diseases in North America (including the

United States), occurring in about 1 of every 2000 Caucasian

births and about 1 of every 250,000 non-Caucasian births.

Even with modern treatment, victims usually die from lung

damage by their early twenties.

If we denote a cystic fibrosis gene with a c and a disease-

free gene with a C (since the disease is recessive), then only a

34.

35. A

o

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