Midterm Review
Name: _______________________________________ per.: ___
1. The Midtown Bank has found that most customers at the tellers’ windows either cash a check
or make a deposit. The chart below indicates the transactions for one teller for one day.
Cash Check
No Check
Totals
Make Deposit
50
20
70
No Deposit
30
10
40
Totals
80
30
110
Find:
P(cash checks ∩ no deposit) =
P(Make Deposit) =
P(Cash Check) =
P(Make Deposit|No Check) =
P(Cash Check|No Deposit) =
If a student were to give 10/40 as an answer to a conditional probability question, what
conditional probability did they find? In other words, P(?? | ??) = 10/40
2. The diagram below shows the number of outcomes (30) in a sample space S and outcomes
in event A and B.
Find each of the following probabilities:
a. P(A∩B) =________
b. P (A) = ________
c. P (B) = ________
d. P(A|B) = ________
f. Are A and B independent events?
Why or why not? (use independence equations to solve)
e. P(B|A) = ________
3. Suppose you conduct a survey where you ask each person two questions. 1) whether they
have cable TV and 2) whether they went on a vacation in the past year. The results are below:
Took a Vacation
Have Cable TV
No Vacation
97
Don't Have Cable TV
Total
Total
135
17
166
Fill out the table. Are the events “choosing a person with cable TV” and “choosing a person who
took a vacation” independent events? Use the equations for independence to solve.
4. A math teacher gave her class two tests. 25% of the class passed both tests and 42% of the class
passed the first test. What percent of those who passed the first test also passed the second test?
5. A jar contains black and white marbles. Two marbles are chosen without replacement. The
probability of selecting a black marble and then a white marble is 0.34, and the probability of
selecting a black marble on the first draw is 0.47. What is the probability of selecting a white marble
on the second draw, given that the first marble drawn was black?
6. At Kennedy Middle School, the probability that a student takes Technology and Spanish is 0.087.
The probability that a student takes Technology is 0.68. What is the probability that a student takes
Spanish given that the student is taking Technology?
7. In a class of 50 students, 18 take Chorus, 26 take Band, and 2 take both Chorus and Band.
Draw a Venn Diagram.
How many students in the class are not enrolled in either class?
What is the probability a student is taking chorus or band?
What’s the probability a student is not taking band or Chorus?
8. Shade the following:
9. Write down the elements in the following sets. Use set notation.
Let U = {0,1,2,3,4,5,6,7,8,9,10}; A = {0,1,2,3,5,8}; B={0,2,4,6}; C = {1,3,5,7}
i) A ∪ B =
ii) B’ =
iii) A ∩ B’ =
iv) B ∪ C =
v) B ∪ C’ =
vi) A’ ∪ C =
vii) (A’ ∩ C) ∪ B =
viii) (A∪B)’ =
ix) (A ∪C) ∩ B
10. A single card is chosen at random from a standard deck of 52 playing cards. What is the
probability of choosing a king OR a club?
11. On New Year's Eve, the probability of a person having a car accident is 0.09. The probability of a
person driving while intoxicated is 0.32 and probability of a person having a car accident while
intoxicated is 0.15. What is the probability of a person driving while intoxicated OR having a car
accident?
12. Amanda used a standard deck of 52 cards and selected a card at random. She recorded the suit
of the card she picked, and then replaced the card back into the deck. The results are below:
Based on her results, what is the experimental probability of selecting a heart?
What is the theoretical probability of selecting a heart?
Based on her results, what is the experimental probability of selecting a diamond or a spade?
What is the theoretical probability of selecting a diamond or a spade?
Compare these results, and describe your findings.