Download Lenarz Math 102 Practice Exam # 3 Name: 1. A 10

Lenarz
Math 102
Practice Exam # 3
Name:
1. A 10-sided die is rolled 100 times with the following results:
Outcome Frequency
1
8
2
8
3
12
4
7
5
15
6
8
7
8
8
13
9
9
10
12
(a) What is the experimental probability of rolling a 5?
(b) What is the theoretical probability of rolling a 5?
(c) What is the experimental probability of rolling a multiple of 3?
(d) What is the theoretical probability of rolling a multiple of 3?
2. One card is drawn from a standard 52 card deck. What is the probability of drawing:
(a) the queen of hearts?
(b) a queen?
(c) a heart?
(d) a face card (J, Q, or K)?
3. Two 6-sided dice are rolled. What is the probability of rolling
(a) a total of 6?
(b) not a total of 6?
(c) total of 6 or 7?
(d) total of 6 or more?
4. A gumball machine has gumballs of five flavors. There are 10 apple, 15 berry, 12 cherry,
8 orange, and 9 mint. When a quarter is put into the machine, it dispenses 5 gumballs
at random. What is the probability that
(a) each gumball is a different flavor?
(b) at least two gumballs are the same flavor?
5. A coin is tossed ten times in a row. Find the probability that
(a) no tails show.
(b) exactly three tails show.
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(c) toss exactly twice as many heads as tails.
6. A group of 15 students is to be split into 3 groups of 5. In how many ways can this be
done?
7. Five cards are drawn from a standard 52 card deck. What is the probability of drawing
(a) 5 cards of the same color?
(b) a full house (3 cards of one rank and two cards of a different rank)?
8. Suppose a jar has 4 coins: a penny, a nickel, a dime and a quarter. You remove two
coins at random without replacement. Let A be the event you remove the quarter. Let
B be the event you remove the dime. Let C be the event you remove less than 12 cents.
(a) List the sample space.
(b) Draw a probability tree diagram to represent the possible scenarios.
(c) Which pair(s) of theses events is (are) mutually exclusive?
(d) Find P (A), P (C), and P (B).
(e) Compute and interpret P (A ∪ B) and P (B ∪ C).
9. A dental assistant randomly sampled 200 patients and classified them according to
whether or not they had a least one cavity in their last checkup and according to what
type of tooth decay preventative measures they used. The information is as follows
Brush only
Brush and floss only
Brush and tooth sealants only
Brush, floss and tooth sealants
At least one cavity
69
34
22
3
No Cavities
2
11
13
46
If a patient is picked at random from this group, find the probability that
(a) the patient had a least one cavity.
(b) the patient brushes only.
(c) the patient had no cavities, given s/he brushes, flosses and has tooth sealants.
(d) the patient brushes only, given that s/he had at least one cavity.
10. A small college has two calculus classes. The first class has 25 students, 15 of whom are
female, and the other class has 18 students, 8 of whom are female. One of the classes is
selected at random and then two students are randomly selected from the class for an
interview. If both of the students are female, what is the probability they came from
the first class?
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11. The probability is 0.6 that a student will study for an exam. If the student studies,
she has a 0.8 chance of getting an A on the exam. If she does not study, she has a
0.3 probability of getting an A. Make a probability tree for this situation. What is the
probability that she gets an A? If she gets an A, what is the conditional probability that
she studied?
12. If you consider the value of a roll of a single 6-sided die to be the number that is rolled,
what is the expected value of the roll of a single die?
13. Consider a game that consists of drawing a single card at random from a standard 52
card deck. You pay $3 to play the game and the $3 is not returned. If you draw an ace
you win $10. If you draw a king or a queen, you win $5. How much should you expect
to win or lose on average if you play this game?
14. Suppose you just inherited $100, 000 and you are trying to decide how to invest it for
the next year. You have narrowed it down to two choices. The first choice is to invest
it in a bond with a guaranteed return of 5% interest at the end of the year. The second
choice is to bet it all on the Super Bowl with a 51% chance of doubling your money and
a 49% chance of losing it all. Which investment option has the highest expected value?