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Chapter 6 Review Quiz
AP Statistics
1.) Brian, who has been randomly selected, is asked to respond yes, no, or maybe to the
question, “Do you intend to vote in the next presidential election?” The sample space is
{yes, no, maybe}. Which of the following represents a legitimate assignment of
probabilities for this sample space?
(A) 0.4, 0.4, 0.2
(B) 0.4, 0.6, 0.4
(C) 0.3, 0.3, 0.3
(D) 0.5, 0.3, -0.2
2.) If Hollie chooses a card at random from a well-shuffled deck of 52 cards, what is the
probability that the card chosen is not a heart?
(A) 0.25
(B) 0.50
(C) 0.75
(D) none of these
3.) Jenna plays tennis regularly with a friend, and from past experience, she believes that
the outcome of each match is independent. For any given match Jenna has a probability
of 0.6 of winning. The probability that Jenna wins the next two matches is
(A) 0.16
(B) 0.36
(C) 0.4
(D) 0.6
(E) 1.2
4.) Event A occurs with probability 0.3 and event B occurs with probability 0.4. If A
and B are independent, we may conclude
(A) P(A and B) = 0.12
(D) all of the above
(B) P(A|B) = 0.3
(C) P(B|A) = 0.4
(E) none of the above
5.) Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B
are disjoint (mutually exclusive) then
(A) P(A and B) = 0.16
(D) P(A or B) = 0.16
(B) P(A or B) = 1.0
(C) P(A and B) = 1.0
(E) none of the above
6.) Jada’s company produces packets of soap powder labeled “Giant Size 32 Ounces.”
The actual weight of soap powder in a box has a normal distribution with a mean of 33
ounces and a standard deviation of 0.7 ounces. What proportion of packets is
underweight (i.e., weighs less than 32 ounces)?
(A) 0.0764
(D) .9236
(B) 0.2420
(E) .0352
(C) .7580
Suppose Emma tosses a coin and rolls a die.
7.) How many outcomes are there?
8.) List the outcomes in the sample space.
9.) Find the probability of Emma getting a head and an even number.
10.) Find the probability of Emma getting a 1, 2, or 3 on the die.
A couple plans to have three children. Find the probability that the children are:
11.) all boys
12.) two boys or two girls
In a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females, and
12 of the juniors are males. If a student is selected at random, find the probability of
selecting
13.) a junior or female
14.) a junior or senior
Eric has applied to both Harvard and the University of Florida. He thinks the probability
that Harvard will admit him is 0.4, the probability that Florida will admit him is 0.5, and
the probability that both will admit him is 0.2. (Eric is very pessimistic. The actual
probability of him being admitted to these schools is significantly higher than stated
here.)
15.) Make a Venn diagram with the probabilities labeled.
16.) What is the probability that neither university admits Eric?
17.) What is the probability that he gets into Florida but not Harvard?
18.) If three dice are rolled, find the probability of getting triples – i.e., 1, 1, 1, or 2, 2, 2,
or 3, 3, 3 etc.
19.) At a self-service gas station, 40% of customers pump regular gas, 35% pump
midgrade, and 25% pump premium gas. Of those who pump regular, 30% pay at least
$20. Of those who pump midgrade, 50% pay at least $20. Of those who pump premium,
60% pay at least $20. Hannah is going to pump gas. What is the probability that she will
pay at least $20? (A tree diagram may be helpful.)
Suppose you are given a standard 6-sided die and told that the die is “loaded” in such a
way that while the numbers 1, 3, 4, and 6 are equally likely to turn up, the numbers 2 and
5 are three times as likely to turn up as any of the other numbers.
20.) The die is rolled once and the number turning up is observed. Use the information
given above to fill in the following table:
Outcome
Probability
1
2
3
4
5
6
21.) Let A be the event: the number rolled is a prime number (a number is defined as
prime if its only factors are 1 and the number itself; note that 1 is not prime). List the
outcomes in A and find P(A).
22.) Let B be the event: the number rolled is an even number. List the outcomes in B
and find P(B).
23.) Are the events A and B disjoint? Explain briefly.
24.) Are the events A and B independent? (Be careful).
25.) Megan is going to draw four cards from a standard deck of 52 playing cards without
replacement, find the probability of her getting at least 1 heart.
A box contains 18 gumballs. Ten of the gumballs are red, five of the gumballs are green,
two of the gumballs are orange, and the last gumball is yellow. Natalie is going to draw
gumballs out of the box without replacement. What is the probability that:
26.) two red gumballs are drawn before any other?
27.) a red gumball is drawn and then the yellow gumball is drawn?
28.) a red and yellow gumball is drawn?
29.) a pink gumball is drawn?
30.) all of the green gumballs are drawn before any other color?
31.) A paper bag contains r red balls and g green balls. If Jason draws two balls with
replacement the probability that he will draw two red balls is the same as the probability
that he will draw one red ball and one green ball. Express g as a function of r (i.e., isolate
g in the equation). (Hint: Use the same thought process that you used above and don’t
let the variables bother you. I know, easier said than done.)