Basic Probability – extra problems
1. The Grade Point Average (GPA) for freshmen was analyzed. On a 4.0 scale, it
was found that 65% of them had GPAs between 1.8 and 3.4; 50% of them
had GPAs between 2.5 and 4.0, and 80% of them had GPAs greater than 1.8.
assign letters to these events. Express each of the following symbolically and
find the probability:
A. The GPA between 2.5 and 3.4
B. The GPA between 1.8 and 2.5
2. A marble is drawn from a bag containing 2 yellow, 5 red, and 3 blue marbles.
a. Find the sample space for this experiment. If you use letters for different
events, explain what these letters represent.
b. Assign probabilities to each individual event in the sample space and explain
how you obtained these probabilities.
c. Find probabilities of the following events:
 The marble drawn is red
 The marble drawn is either yellow or blue
 The marble drawn is green
 The marble drawn is red or yellow or blue
3. Decide whether the events listed below are mutually exclusive (disjoint):
a. Being 15, being a teenager
b. Wearing jogging shoes, wearing sandals
c. Being a female, being a dancer
d. Owning a bicycle, owning a car
e. Being a U.S. Senator, being a U.S. Congressman concurrently
4.
a. Given P(A)=.5, P(B)=.35, Can P(AUB)=.85? Explain.
b. Given P(A)=.5, P(B)=.35, Can P(AUB)=.90? Explain
c. Given P(A)=.5, P(B)=.35, Can P(AUB)=.65? Explain.
5. A card is drawn at random from a well-shuffled standard deck of 52 cards. Find
each of the following probabilities:
a. The card drawn is a face card
b. The card drawn is red
c. The card drawn is a black 3
d. The card drawn is a club or red
e. The card drawn is not a face card
f. The card drawn is not a club and is not red
6. The management of a firm wants to survey its workers, who are classified as
follows:
30% have worked for the company for 5 years or more, 28% are female, and 65%
contribute voluntarily to a retirement plan. 1/2 of the female workers contribute to
the retirement plan. Find the following probabilities assuming one individual
worker is chosen at random:
a. A male worker is selected.
b. A worker with less than 5 years in the company is selected
c. A worker who contributes to the retirement plan or a female worker is
selected
**HINT: Draw a Venn Diagram and highlight the regions corresponding the events
given in a-c.
7. A group of 60 freshman business students at a large university was surveyed,
with the following results:
19 of the students read Business Week
18 of the students read The Wall Street Journal
50 read Fortune
13 read Business Week and The Wall Street Journal
11 read The Wall Street Journal and Fortune
13 read Business Week and Fortune
9 read all three
Draw a Venn Diagram Displaying this information and answer the following:
a. How many students read none of the 3 publications?
b. How many read Fortune only?
c. How many read Business Week and The Wall Street Journal, but NOT
Fortune?
8.
Suppose the probability that a jury would acquit a randomly chosen defendant
is 0.34 and the probability that a judge would acquit a randomly chosen
defendant is 0.18. In addition, suppose the probability that both the jury and
the judge would acquit a randomly chosen defendant is 0.15. Find probabilities
of the following events:
a. The jury would not acquit a randomly chosen defendant.
b. Neither the judge nor the jury would have acquitted a randomly chosen
defendant.
c. The jury would have acquitted a defendant, but the judge would not.
Some answers:
4.
(a) yes
5.
(a) 3/13
6.
(a) 0.72
7.
(a) 1
8.
(a) 0.66
(b) no
(b) 1/2
(b) 0.7
(b) 35
(b) 0.63
(c) yes
(c) 1/26
(c) 0.79
(c) 4
(c) 0.19
(d) 3/4
(e) 10/13
(f) 1/4