The Probability Game
Week 6, Wednesday
Teams
Group 1
Caleb, Snyder
Tiffany, Anderson
Samuel, Hodous
Lauren, Dougherty
David, Boor
Group 4
Katelyn, Giles
Bobbi, Brown
Nicholas, Saltis
Vesna, Jankovic
Alex, Tomcany
Group 2
Brandon, Bradford
Joseph, Tait
Allison, Blake
Melissa, Miller
Kyle, Radford
Group 5
Richard, Bacher
Brittney, Fraley
Nicole, Klejka
Daniel, Campolito
Melissa, Sturdivant
Group 3
Danielle, King
Stephanie, Smith
Angie, Stegenga
Stephen, Pero
Rebecca, Barnes
Group 6
Sarah, Baker
Hannah, Goodrick
Alison, Clement
Evan, Warrick
Eldin, Becirovic
This game affects your Quiz 4 Grade
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First place: +4 points
Second place: +3 points
Third place: +2 points
Fourth place: +1 point
Fifth place: +0 points
Last place: -1 point
** You can’t earn more than 10/10 on quiz 4 **
Study These Questions
• Most of these questions are similar to the
questions you’ll find on midterm #2!!!
Rules
• There are 7 questions, and they will appear on
the screen one at a time.
• For each question, the group will discuss the
solution, and the Team Captain will record a
single answer and hand the paper into me.
• We will discuss the solution as a group, and the
paper will be handed back for the next question
to be answered.
• The order of winners is decided by the number
of correct answers each team provides.
Question #1
Question: Which of these probability assignments are possible?
Assignment A
X
0
1
2
3
P[X]
25%
25%
25%
25%
Assignment B
X
1
2
3
4
Answer: A, B, C
P[X]
20%
30%
30%
20%
Assignment C
Assignment D
X P[X]
0 100%
1 0%
2 0%
3 0%
X P[X]
0 -5%
1 5%
2 100%
3 0%
Assignment E
X
0
1
2
3
P[X]
10%
30%
40%
50%
Question #2
Question: In a standardized test 80% of the students pass.
Three students take the test. What is the probability that:
(a) All three pass
(b) None pass
(c) At least one passes
Answer:
(a) P[1p and 2p and 3p] = P[1p]*P[2p]*P[3p] = .8*.8*.8 = 51%
(b) P[1f and 2f and 3f] = P[1f]*P[2f]*P[3f] = .2*.2*.2 = .8%
(c) P[At least one passes] = 1 – P[nobody passes] = 99.2%
Question #3
Question: Let X represent the number of fights at “Tiny Tavern”
during a week. The following lists the probability model for X:
X
0
1
2
P[X] 50% 30% 10%
3
4
5
?
3%
2%
(a) Find P[more than 2 fights this week]
(b) Find P[6 fights this week]
Answer:
(a) P[more than 2 fights this week] = P[3]+P[4]+P[5] = 10%
(b) P[6 fights this week] = 0%
Question #4
Question: Let X represent the number of fights at “Tiny Tavern”
during a week. The following lists the probability model for X:
X
0
1
2
P[X] 50% 30% 10%
Calculate
Answer:
3
4
5
?
3%
2%
  E X    x P X  x
X
0
1
P[X] 50% 30%
xP[x]
0
.3
2
10%
3
?
4
3%
5
2%
.2
.15
.12
.1
E[X] = 0 + .3 + .2 +.15 + .12 + .1 = .87
Question #5
Question: Administration wants to find out if UA students felt
appreciated on Student Appreciation Day. To do this they
randomly select students and surveyed them about the
experience. Suppose the data are gathered and summarized
in the table below. (a) Find P[Appreciated | Grads]
and (b) P[Appreciated]. (c) Can you conclude independence?
Undergrad
Grad
Answer:
Felt Appreciated?
Yes
No
100
250
50
125
P[A | G] = 50/175 = 28.6%.
P[A] = 150/525 = 28.6%. (equal therefore indep.)
Question #6
Question: For the following two situations, list all of the
outcomes in the sample space and tell whether the outcomes
are equally likely:
(a) Flip a coin until you observe a tail or have four tosses.
(b) Toss the coin four times and record the number of tails.
Answer (a): {T, HT, HHT, HHHT, HHHH}. These outcomes are
not equally likely – for example, the probability of flipping a
tails on the first try is 50%, but the probability of flipping four
heads in a row is much smaller.
Answer (b): {0, 1, 2, 3, 4}. These outcomes are not equally
likely. This is a binomial distribution with n=4 and p=50%.
Question #7
Question:
(a) How many binomial distributions exist?
(b) What two things do you need to know in order to identify the exact
binomial distribution needed to solve a given problem?
(c) A telemarketer makes 1,000 phone calls per day. The probability
that he will make a sale to a given person is 0.5%. Assume each
person he calls is independent of the others. Define a random
variable, X, as the number of sales made in a given day. Is this
binomial? If so, what is the mean and variance of X?
Answer (a): Infinite. For every n and p, there is a unique
binomial distribution.
Answer (b): n (number of trials) and p (probability of success)
Answer (c): Binomial. E[X] = np = 1000(.005) = 5.
VAR[X] = npq = 1000(.005)(.995) = 4.98