7/27/2019 Praxis Probability
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Problem #6
PRAXIS - WI
Jarod Hart
Maren Lau
Kristin Radermacher
Cheslea Simon
If a students takes a test consisting of 20
true-false questions and randomly guesses at
all of the answers, what is the probability that
all 20 guesses will be correct?
a. 0
b. (1/2)20
c. 1/(2*20)
d. 1/2
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If a students takes a test consisting of 20
true-false questions and randomly guesses
at all of the answers, what is the
probability that all 20 guesses will be
correct?
a. 0
b. (1/2)20
c. 1/(2*20)
d. 1/2
Problem Name
The probability of multiple
independent events is the product
of the probabilities of the events.
What is the probability of getting 2 right out of 3 true-
false questions?
The possible combinations are (R right, W wrong):
{(R,R,W),(R,W,R),(W,R,R)}
The probability of getting 2 out of 3 right is:
p=p(R,R,W)+p(R,W,R)+p(W,R,R)
=1/8+1/8+1/8=3/8
The user should be able to put a number 0, 1, 2, or 3 in place of the red
underlined number. All of the blue output should change when that number is
entered. If a 1 is entered, the only thing in the output that will change is the
combinations. All of the values will stay the same, just replace the
combinations from two right to only 1.
a. Incorrect, there is positive
probability of answering all 20
correctly
b. Correctc. Incorrect, remember that each
question is an independent
event
d. Incorrect, that is the probability
of getting one question right
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If a students takes a test consisting of 20
true-false questions and randomly guesses
at all of the answers, what is the
probability that all 20 guesses will be
correct?
a. 0
b. (1/2)20
c. 1/(2*20)
d. 1/2
Problem Name
The probability of multiple
independent events is the product
of the probabilities of the events.
What is the probability of getting 0 right out of 3
true-false questions?
The possible combinations are:
{(W,W,W)}
The probability of getting 2 out of 3 right is:
p=p(W,W,W)=1/8
This is the output that should be produced when a 0 is entered. Similarly, if
a 3 is entered, all that will change is (W,W,W) will become (R,R,R).
a. Incorrect, there is positive
probability of answering all 20
correctly
b. Correctc. Incorrect, remember that each
question is an independent
event
d. Incorrect, that is the probability
of getting one question right
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Problem Name
To find this probability, we can find the
total number of ways to get all problems
correct, and then divide that by the total
number of possible outcomes. This
technique applies when you are workingwith equally likely outcomes. Our equally
likely outcomes are getting an individual
problem right or wrong, each with
probability .
Tutorial
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Problem Name
To find this probability, we can find the
total number of ways to get all problems
correct, and then divide that by the total
number of possible outcomes. This
technique applies when you are workingwith equally likely outcomes. Our equally
likely outcomes are getting an individual
problem right or wrong, each with
probability .
There is only one possible combination of
events that results with all 20 questionsright. That is 20 right and 0 wrong.
Tutorial
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Problem Name
To find this probability, we can find the
total number of ways to get all problems
correct, and then divide that by the total
number of possible outcomes. This
technique applies when you are workingwith equally likely outcomes. Our equally
likely outcomes are getting an individual
problem right or wrong, each with
probability .
There is only one possible combination of
events that results with all 20 questionsright. That is 20 right and 0 wrong.
Now we have to find the total number of
possible outcomes. For the first problem,
there are two outcomes, right or wrong.
Tutorial
right
wrong
1st question
2 outcomes
7/27/2019 Praxis Probability
7/21Problem Name
To find this probability, we can find the
total number of ways to get all problems
correct, and then divide that by the total
number of possible outcomes. This
technique applies when you are workingwith equally likely outcomes. Our equally
likely outcomes are getting an individual
problem right or wrong, each with
probability .
There is only one possible combination of
events that results with all 20 questionsright. That is 20 right and 0 wrong.
Now we have to find the total number of
possible outcomes. For the first problem,
there are two outcomes, right or wrong.
Tutorial
right
wrong
1st question
2 outcomes
right
wrong
1st question
2 outcomes 22 outcomes
2nd question
right
right
wrong
wrong
Then for two problems there
are four possible outcomes.
7/27/2019 Praxis Probability
8/21Problem Name
To find this probability, we can find the
total number of ways to get all problems
correct, and then divide that by the total
number of possible outcomes. This
technique applies when you are workingwith equally likely outcomes. Our equally
likely outcomes are getting an individual
problem right or wrong, each with
probability .
There is only one possible combination of
events that results with all 20 questionsright. That is 20 right and 0 wrong.
Now we have to find the total number of
possible outcomes. For the first problem,
there are two outcomes, right or wrong.
Tutorial
For each question, the number
of possible outcomes doubles.
right
wrong
1st question
2 outcomes
right
wrong
1st question
2 outcomes 22 outcomes
2nd question
right
right
wrong
wrong
Then for two problems there
are four possible outcomes.
right
wrong
1st question
2 outcomes 22 outcomes
2nd question
right
right
wrong
wrong
23 outcomes
right
right
right
right
wrong
wrong
wrong
wrong
3rd question
220 outcomes
20th question
7/27/2019 Praxis Probability
9/21Problem Name
To find this probability, we can find the
total number of ways to get all problems
correct, and then divide that by the total
number of possible outcomes. This
technique applies when you are workingwith equally likely outcomes. Our equally
likely outcomes are getting an individual
problem right or wrong, each with
probability .
There is only one possible combination of
events that results with all 20 questionsright. That is 20 right and 0 wrong.
Now we have to find the total number of
possible outcomes. For the first problem,
there are two outcomes, right or wrong.
Tutorial
right
wrong
1st question
2 outcomes 22 outcomes
2nd question
right
right
wrong
wrong
23 outcomes
right
right
right
right
wrong
wrong
wrong
wrong
3rd question
220 outcomes
20th question
For each question, the number
of possible outcomes doubles.
right
wrong
1st question
2 outcomes
right
wrong
1st question
2 outcomes 22 outcomes
2nd question
right
right
wrong
wrong
Then for two problems there
are four possible outcomes.
Then for 20 questions the total number of
outcomes will be 2*2**2=220.
Then the probability of getting all 20 problems
correct is 1/(220)=(1/2)20. So the correct answer
is B.
7/27/2019 Praxis Probability
10/21Problem Name
To find this probability, we can find the
total number of ways to get all problems
correct, and then divide that by the total
number of possible outcomes. This
technique applies when you are workingwith equally likely outcomes. Our equally
likely outcomes are getting an individual
problem right or wrong, each with
probability .
There is only one possible combination of
events that results with all 20 questionsright. That is 20 right and 0 wrong.
Now we have to find the total number of
possible outcomes. For the first problem,
there are two outcomes, right or wrong.
Tutorial
right
wrong
1st question
2 outcomes 22 outcomes
2nd question
right
right
wrong
wrong
23 outcomes
right
right
right
right
wrong
wrong
wrong
wrong
3rd question
220 outcomes
20th question
For each question, the number
of possible outcomes doubles.
right
wrong
1st question
2 outcomes
right
wrong
1st question
2 outcomes 22 outcomes
2nd question
right
right
wrong
wrong
Then for two problems there
are four possible outcomes.
Then for 20 questions the total number of
outcomes will be 2*2**2=220.
Then the probability of getting all 20 problems
correct is 1/(220)=(1/2)20. So the correct answer
is B.
7/27/2019 Praxis Probability
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Since the result of any question has no impact on
the result of any of the other questions, the two
event are said to independent
R and W are independent
Then we know that the probability of two
independent events is the product of the
probabilities of the individual events. Then the
probability of getting two problems right
2R two out of two questions rightP(2R)=P(R)*P(R)=(P(R))2=(1/2)2
Then we can find the probability of getting all 20
right in the same way
20R 20 out of 20 questions rightP(20R)=(P(R))20=(1/2)20
Then the answer is B, to the twentieth
B (1/2)20
If a students takes a test
consisting of 20 true-false
questions and randomly
guesses at all of the answers,
what is the probability that all 20guesses will be correct?
a. 0
b. (1/2)20
c. 1/(2*20)
d. 1/2
We can define two events for this problem.
One event is getting a problem right. The
other event will be getting a problem wrong
R Answer a question right
W Answer a question wrong
The probability of each of these events is one
half
P(R)=1/2
P(W)=1/2
7/27/2019 Praxis Probability
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Jill has two different pairs of pants, 3 different pairs of sock and 5 different
pairs of shoes. Assuming Jill wears matching socks and matching shoes,
how many different combinations of pants, socks and shoes can she wear?
Problem Name
A
Thats right.
Remember the multiplier rule.
Remember the multiplier rule.
Remember the multiplier rule.
A. 30 *
B. 10
C. 21
D. 38
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BWhat is the probability of rolling a 4 or a 5 with one role of a fair 6 sided
die?
The probability of rolling a 4 is 1/6 and
the probability of rolling a 5 is 1/6
Thats right.
A 4 or a 5, not and.
The probability of each number on the die is
1/6
A. 1/6
B. 1/3 *
C. 1/36
D. 1/18
7/27/2019 Praxis Probability
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CJohn rolls two dice, and examines the sum of the rolled values. Which
value is the least likely to be the sum of the two dice?
Think of the possible ways to roll each
value
Think of the possible ways to roll
each value
Think of the possible ways to roll
each value
Thats right
A. 6
B. 5
C. 8
D. 12 *
7/27/2019 Praxis Probability
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DA student is taking a 20 question true false test. The students knows the
material well enough to have a 2/3 chance of getting each problem right.
What is the probability that the students gets all 20 correct?
That is the probability of getting an
individual question right, not all
Thats right The probability of a series of independent
events is the product of their probabilities
A. 2/3
B. (2/3)20 *
C. (1/2)20
D. 20*2/3
The probability of getting each problem right
is 2/3
7/27/2019 Praxis Probability
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EDavid and Todd are playing the card game Hearts. In the game of Hearts, it
is typically a disadvantage to be dealt the Queen of Spades. What is the
probability that in all 6 hands they play, that Todd will be dealt the Queen of
Spades?
That is the probability for one hand
There is a positive probability of
being dealt the Queen of Spades
The probability of a series of
independent events is the product of
their probabilities
Thats right
A. 1/52
B. 0
C. 52(1/6)
D. (1/52)6 *
7/27/2019 Praxis Probability
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FA bag contains 50 different colored balls: 10 green, 20 pink, 15 blue, and 5
yellow. If you draw 5 balls from the bag without replacement, what is the
probability that all of the balls you draw out are yellow?
That is the probability of the first yellow
ball
The balls are not being put back into
the bag
Thats right
When a ball is taken out, the total number of
balls changes
A. 5/50
B. (5/50)5
C. (5/50)*(4/49)*(3/48)*(2/47)*(1/46) *
D. (5/50)*(4/50)*(3/50)*(2/50)*(1/50)
7/27/2019 Praxis Probability
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GIf you roll a dice 10 times in a row, what is the probability of rolling ten 1s?
The probability of rolling a 1 on a given
roll is 1/6
The probability of a series of
independent events is the product of
their probabilities
The probability of rolling a 1 on a
given turn is 1/6
Thats right
A. 1/10
B. 1/60
C. (1)10
D. (1/6)10 *
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Problem Name
HIf you roll a dice 10 times in a row, what is the probability of not rolling any
6s?
It is possible to not roll any 6s
Thats right
The probability of rolling a 1 on a
given turn is 1/6, what is the
probability of not rolling a 1.
That is the probability of not rolling a 1 on one
roll
A. 0
B. (5/6)10 *
C. (1/6)10
D. 5/6
7/27/2019 Praxis Probability
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Problem Name
IAn M&M bag contains 10 red candies, 14 brown candies, and 8 green
candies. You reach in and grab 1 candy, record the color then put it back in
the bag. Then you repeat the process 3 more times. What is the
probability that you recorded 4 brown candies?
Thats right
The three colors are not equally
likely to be chosen
The probability of a series of
independent event is the product of
the probability of the events
That is the probability of recording a brown
with one draw, not 4
A. (14/32)4 *
B. (1/3)4
C. 4(1/3)
D. 4/32
Type feedback for answers in text boxes below.
7/27/2019 Praxis Probability
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Problem Name
JWhen playing poker, a flush is a hand of 5 cards of the same suit. With a
standard deck of cards, you are dealt 5 cards at random. What is the
probability that you have a flush of Hearts?
There are 13 Hearts in a standard
deck of cards
The cards are being dealt without
replacement
Thats right
The total number of cards is changing as the
cards are being dealt
A. (1/52)5
B. (13/52)5
C. (13/52)*(12/51)*(11/50)*(10/49)*(9/48) *
D. (13/52)*(12/52)*(11/52)*(10/52)*(9/52)