__
Probability Review Questions
1. Find the following theoretical probabilities:
a. You roll a number cube numbered from 1 to 6. P(a number greater than 5).
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b. A number from 18 to 25 is drawn at random. P(22).
c. A jar contains 7 green, 19 black, and 13 pink marbles. A marble is drawn at
random. P(not pink).
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d. A number from 20 to 29 is drawn at random. P(a number divisible by 2).
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2. Find the following empirical (experimental) probabilities:
a. Dylan lives in Montana. On a bus trip across the state he looks out the window
and sees where other vehicles are from. On the trip he sees 125 vehicles with
Montana plates and 40 with non-Montana plates. On the trip back the next
day, what is the probability that the first car he sees is from Montana?
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b. Noah counts the grassho
1nthãidëiiöiiMöhday. He finds nineteen big
ones and nine small ones. On Tuesday he counts them again. This time he
counts a total of eighty-seven grasshoppers. What is a reasonable prediction to
make as to how many of the grasshoppers were large ones when he counted
them on Tuesday?
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c. Kayla has taken twenty-nine math quizzes this year. Of those, she scored
above 90% on five of them and 80% or above on fourteen of them. What is
the probability that she will score from 80% to 90% on her next math quiz?
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3. Luis does not know the answer to two questions on a multiple choice exam. The first
question has four choices and the second question he does not know has six choices.
What is the probability that he will get both questions wrong?
P(t)
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4. What is the probability, that on two consecutive rolls of a die, fiitahôddrthniber,
then an even number will come up?
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.
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You have five penmes eight nickels and four dimiiäpijy bink If you turn the
bank upside down and shale it until a coin comes out of the slot, what is the
probability that you will get two pennies in a row?
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6. You roll a number cube numbered from 1 to 6. You then spin a spinner with 3
sections each with a different color. The spinner has the colors orange, gray, and
pink. P(2, 4, 1, 5, or 3 and orange)
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7. There are 5 brown, 6 red, and 4 white marbles in a hat. You pick 4 marbles from the
hat. Marbles are n returneçl after they have been drawn.
\ P(four white marbles in a row)
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8. You roll a cube which has the numbers 16, 18, 24, 18, 24, and 26 on it. You then spin
a spinner which has 5 sections. The letters on the spinner are F, H, H, and H.
P(a number less than 24 and not F)
,
___
9. There are 4 yellow, 6 black, and 4 pink marbles in a hat. You pick 3 marbles from the
hat. Marbles are potreimed after they have been drawn. P(the first marble is black,
the second marble is not pink, and the third marble is pink)
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10. You flip a coin and toss a 1-6 number cube. P(not tails and nota3y--—----”
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11. From foig men and two women, a committee is formed by drawing three names out
of a hat. What is the probability that all three names drawn are those of men if the
names are not cRiaced after being drawn?
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12. The following table shows the data collected from a clinical trial ofablood test for
limes disease.
Positive Test Result
(lymes disease is
indicated)
92
6
Subject has lymes disease
Subject does not have lymes
disease
Negative Test Result
(lymes disease is not
indicated)
7
16
a. If one subject is randomly selected, what is the probability that they tested
negative or has lymes disease?
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b. If two different subjects are randomly selected, find the probability that they
both have lymes disease.
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c. If one subject Irandoriily selected, find the probabiliththejtésTed
negative and is does not have lymes disease.
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Combinations and Permutations
1.
The school board has seven members. The
board must have three officers: a chairperso
n, an
assistant chairperson, and a secretary.
—
a
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a. How many different sets of these officers can
be formed from this board?
b. How many three-person committees can be
formed from this board?
2. Ralph Simpson has room for three plants
on a windowsill.
a. In how many different ways can three plan
ts be arranged on his windowsill?
b. Suppose Ralph has six plants. How many
ps of three plants can be put on his windowsi
ll?
-
c. Suppose Ralph has nine plants. How man
y ways can three of these plants be arranged
on his
windowsill?
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3. To open your locker, you must dial a sequence
of three numbers called the lock’s combination.
Given that there are 40 numbers on a lock, how
many different locker combinations are there
?
4. Suppose fifteen people qualify for a colle
ge cheerleading squad, six women and nine men
.
a. How many six-member squads can be selec
ted?
b. Supposethat Itwo members of the
six-member squad must be male. How many
six
member squads can be selected?
3 \b
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c. Find the probability of the event in part (b)
if you were to pick the squads randomly.
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ning to give a performance. One of the pieces
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6. Ophelia Payne has 35 CD’s and two different CD
players. Upstairs, she has a 6-disc changer.
Downstairs she has a 20-disc changer.
a. If she plans to play the 6 discs straight through
starting on the first disc in the chamber, how
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into her upstairs changer?
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the downstairs player on “shuffle” mode?
e. In her car, Ophelia has a single disc player. Curr
ently in her player is the “new” Red Hot Chili
Peppers disc. This disc has 13 ts. Ophelia hits
the “random play” button which will
randomly arrange the 13 trd1nto an order. Wha
t is theprobability that the tracks will play
in the original order (1, 2, 3, 4,
13)?
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