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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