Riva – Adv Precalc
Chapter 8 (Part II) Review
1) Calculate the following by hand (on the test, to get full credit, you need to
show your work so that I know you did it by hand)
a. 15 C3
b. 12 P5
æ 9ö
c. ç ÷
è 3ø
2) On a single toss of a die, what is the probability of obtaining the following
a. An even number
b. A number greater than 4
3) Four fair coins are tossed
a. Find the sample space
b. Find the probability that 2 or more heads come up
c. Find the probability of getting at least one tail
4) Use the following table to answer the questions. This table shows the number
of correctly and incorrectly filled out tax forms obtained from a random
sample of 100 returns examined by the Internal Revenue Service (IRS) in a
recent year
Correct
Incorrect
Totals
Short Form (1040 A)
No Itemized
Deductions
15
5
20
Long Form (1040)
No Itemized
Deductions
40
20
60
Long Form (1040)
Itemized Deductions
Totals
10
10
20
65
35
100
a. Find the probability that a form was a long form (1040)
b. Find the probability that a form was an incorrectly filled out short
form (1040A)
c. Find the probability that a form was correctly filled out given that it
had itemized deductions
d. Find the probability that the form was a long form (1040) given that it
was incorrectly filled out
5) There is an urn containing five $50 bills, four $20 bills, three $10 bills, two $5
bills, and one $1 bill. A person draws out three bills. Find the following
a. The probability of selecting three $20 bills with replacement
b. The probability of selecting three $20 bills without replacement
c. The probability of selecting exactly two $50 bills without replacement
d. The probability of first selecting a $50, then a $20 bill, then a $50 bill
(in that order) without replacement
e. The probability of selecting at least two $20 bills without replacement
f. The probability of first selecting a bill over $10, then a bill over $5,
then a $50 bill (in that order) without replacement
6) An agent sells life insurance policies to five equally aged, healthy people.
According to recent data, the probability of a person living in these
conditions for 30 years or more is 2/3. Calculate the probability that after 30
years:
a. All five people are still living.
b. At least three people are still living.
c. Exactly two people are still living
Riva – Adv Precalc
7) Arizona’s “Fantasy Five” is a 5/45 lottery (i.e., you choose five distinct
numbers between 1-45). To win, you must select all five of the winning
numbers. Find the probability that you win.
8) A player throws a die. If a prime number is obtained, he gains to win an
amount equal to the number rolled times 100 dollars, but if a prime number
is not obtained, he loses an amount equal to the number rolled times 100
dollars. Calculate the probability distribution and the expected value of the
described game.
9) In 2004, the Center for Disease Control estimated that 1,000,000 of the
287,000,000 residents of the U.S. are HIV-positive. The SUDS diagnostic test
correctly diagnoses the presence of AIDS/HIV 99.9% of the time and
correctly diagnoses its absence 99.6% of the time
a. Find the probability that a person whose test results are positive
actually has HIV
b. Find the probability that a person whose test results are negative
actually has HIV
c. Find the probability that a person whose test results are positive does
not have HIV
d. Find the probability that a person whose test results are negative does
not have HIV
10)Venus Williams learned to play tennis at a public park in Compton, CA. She
now competes in professional tennis tournaments around the world. On each
point in tennis, a player is allowed two serves. Suppose while playing tennis,
Venus gets her first serve in about 75% of the time. When she gets her first
serve in, she wins the point about 80% of the time. If she misses her first
serve, her second serve goes in about 90% of the time. When this happens,
she wins the point on her second serve about 35% of the time.
a. Draw a tree diagram that represents all possible situations
b. Find the probability that Venus wins a point when she is serving
c. Find the probability that Venus will win the point given that she gets
one of her serves in.
d. If you know she won a point while serving, what is the probability that
she made her first serve?
11)A medical research lab proposes a screening test for a disease. To try out this
test, it is given to 100 people, 60 of whom are known to have the disease and
40 of whom are known not to have the disease. A positive test indicates the
disease and a negative test indicates no disease. Unfortunately, the test is
negative for 2 of the 60 people who do have the disease, and the test is
positive for 10 of the 40 people who do not have the disease. Suppose the test
is given to a person whose disease status is unknown
a. If the test is negative, what is the probability that the person does not
have the disease?
b. If the test is positive, what is the probability that the person has the
disease?
12)The first prize for a raffle is $5,000 (with a probability of 0.001) and the
second prize is $2,000 (with a probability of 0.003). What is a fair price to
pay for a single ticket in this raffle?
13)You decide to tell your fortune by drawing two cards from a standard deck of
52 cards. What is the probability of drawing two cards of the same suite in a
row?
Riva – Adv Precalc
14)As accounts manager in your company, you classify 75% of your customers
as "good credit" and the rest as "risky credit" depending on their credit
rating. Customers in the "risky" category allow their accounts to go overdue
50% of the time on average, whereas those in the "good" category allow their
accounts to become overdue only 10% of the time. What percentage of
overdue accounts are held by customers in the "risky credit" category?
15)A card is drawn randomly from a deck of ordinary playing cards. You win $10
if the card is a spade or an ace. What is the probability that you will win the
game?
16)Marie is getting married tomorrow, at an outdoor ceremony in the desert. In
recent years, it has rained only 5 days each year. Unfortunately, the
weatherman has predicted rain for tomorrow. When it actually rains, the
weatherman correctly forecasts rain 90% of the time. When it doesn't rain,
he incorrectly forecasts rain 10% of the time. What is the probability that it
will rain on the day of Marie's wedding?
Chapter 8 (Part II) Review
Riva – Adv Precalc
15!
15 ×14 ×13
=
= 455
(15 - 3)!3!
3!
12!
= 12 ×11×10 × 9 × 8 = 95040
b. 12 C5 =
(12 - 5)!
9!
9×8×7
æ 9ö
=
= 84
c. ç ÷ =
3!
è 3ø (9 - 3)!3!
2) a. 1/2
b. 1/3
3) a. {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT,
THTH, THTT, TTHH, TTHT, TTTH, TTTT}
b. 11/16
c. 15/16
4) a. 4/5
b. 1/20
c. 1/2
d. 6/7
5) a. 64/3375 b. 4/455
c. 20/91
d. 8/273
e. 2/13
f. 40/273
6) a. 32/243
b. 64/81
c. 40/243
7) 1/1221759
8) 1/6: -$100, 1/6: +$200, 1/6: +$300, 1/6: -$400, 1/6: +500, 1/6: -$600
Expected Value: -$16.67
9) a. 0.466
b. 0.00000351
c. 0.534
d. 0.99999649
10) a.
1) a.
15
C3 =
b. 543/800
11) a. 15/16
12) $11
13)4/17
14)5/8
15)4/13
16).111
c. 181/260
b. 29/34
d. 160/181