AP Statistics Probability Assessment
Name: _______________________________
Kylie yap
Answer each question completely. You must label each answer clearly (ex. P(A or B) = 0.03) If you do not show work for a
particular question, you will not be awarded any points for that question.
For questions 1-7: A statistics teacher has 65 students in his class, 36 juniors and the rest are seniors. At the beginning of
class on a Monday, the teacher planned to spend time reviewing an assignment due that day. Unknown to the teacher, only
20 of the juniors and 10 of the seniors had completed the assignment. The teacher plans to randomly select students to do
problems from the assignment on the whiteboard.
1.
Build a Venn Diagram or 2 way table from this information (5 points).
d
10
s
c completed
n notcompleted
inn.nl
2.
3.
4.
IY q l
senior
senior
j junior
What is the probability that a randomly selected student has completed the assignment? (2 points)
Po
38 0.46
_____________
0.46
PC
Given a student has completed the assignment, what is the likelihood that the student is not a junior? (3 points)
Pfj C 38
0.33
_____________
C 0.33
Pfj
What is the probability that a randomly selected student in this class is not a junior? (2 points)
PCT 38 0.55
PCT I 0.55 0.45
5.
_____________
P1
j 0.45
Based on your answers to the previous two parts, can you state that “Not a junior” and “Completed Assignment” are
independent? Explain why or why not, and include mathematical evidence. (5 points)
PC j C
P j
0.33 0.45
Notajunior and completedassignment are not
independent If theywereindependent then
Pti o PC but they'retwo different probabilities
6. Using your answer from #2 as the probability of success, describe how to use a table of random digits to simulate the
likelihood that 2 or more of 4 randomly selected students completed the assignment. (4 points)
Plo 0.46 Es
1
Assignnumbers01to 30 for completed assignments and 31 to 65 as
didn'tcomplete
2 Select 4 unique 2
digit numbersfrom01 to 65
3 Record howmany students completed the
assignment
7.
Complete three repetitions of your simulation using the random digits below and use the results to estimate the
probability described in the previous question. Begin at the top left of the table. (2 points per trial)
0077707
ODAQfoy
51
24
22
08
34
25
_____________ _____________ _____________
OF
_____________ _____________ _____________
IT
_____________ _____________ _____________
Trial 1: ____________
Trial 2: ____________
Trial 3: ____________
1001
43
P(2 or more) = ____________
33 1
T
372
22
54
372
3
2
For #8-#11: A weighted number cube comes up pips (or spots) with the following probabilities:
P(1) = 0.20
P(2) = 0.10
P(3) = 0.25
P(4) = 0.25
P(5) = 0.15
P(6) = 0.05
8.
If one of these cubes is thrown, what is the probability that the roll is an even number? (2 points)
PLZ or 4016
P 2 P 4 PCG
0.10 0.25 0.05 0.4
9.
_____________
Pleven
0.4
If two of these number cubes are thrown, what is the probability the sum is at most 10? Show work. Hint: use a
complement (4 points)
2 345.67.8.9 10.11.12
Plsummorethan101
4 0.18
Plsumatmost107 1 0.18 0.82
_____________
Plsumatmost
01 0.82
10. If two of these number cubes are thrown, what is the probability that their product is 12? Show work. (4 points)
3
551
14 1 4 8.1 8 588
P 260123,47 0.005 0.625 0.63
is127 0.63
Pproduct_____________
11. Mrs. Vaccaro rolls this number cube and covers the pips. She will only tell you that the roll is even. What is the
probability that the outcome is 6, given it is even? Show work (4 points)
Pleven a
Plergygnd
0
05.05
0.4
Even 67 0.4
P _____________
For #12-15: If a person drives a hybrid vehicle, there is an 80% chance they bring their own bags to the grocery store. About
17% of all cars are hybrid. If a person doesn’t drive a hybrid, there is a 55% chance they won’t bring their own bags to the
grocery store either.
12. Build a tree diagram of this scenario, labeling branches with outcomes and probabilities (5 points).
h hybrid
n nonhybrid
b bringbag
d doesn'tbring
h
handb
0.136
a PChandd 0.034
5 Plnand b 0.3735
17
ng
Is P nanda 0.4565
13. What is the probability that a randomly selected person brings their own bags to the grocery store? Show work (4
points)
Pb
Plnand b
5854331858
as
P hand b
pistol
_____________
Pcb
0.5095
14. What is the probability that a randomly selected person drives a hybrid vehicle and brings their own bags to the
grocery store? Show work (4 points)
P hand b
P hand b
Plh x P b
17 8 0.136
_____________
b 0.136
P hand
15. What is the probability that a randomly selected person drives a hybrid or brings their own bags to the grocery
store? Show work (4 points)
Plh tP b P horb
17 0.5095 17 0.5095
overlap
_____________
PChorb
0.5095