STAT/MA 41600
Practice Problems: September 5, 2014
1. Choosing a page at random.
A student buys a brand new calculus textbook that has 1000 pages, each numbered with
3 digits, from 000 to 999. She ran
STAT/MA 41600
In-Class Problem Set #9: September 15, 2014
Solutions by Mark Daniel Ward
1a. The joint mass is pX,Y (1, 1) = (3/5)(2/4) = 3/10, pX,Y (1, 0) = (3/5)(2/4) = 3/10,
pX,Y (0, 1) = (2/5)(3/4)
STAT/MA 41600
In-Class Problem Set #9: September 15, 2014
1. Suppose Alice and Bob each take a cookie, without replacement, from a jar that contains
5 cookies, 3 of which are chocolate, and the other
STAT/MA 41600
Practice Problems: September 15, 2014
Solutions by Mark Daniel Ward
1. Butteries. Alice, Bob, and Charlotte are looking for butteries. They look in three
separate parts of a eld, so that
STAT/MA 41600
Practice Problems: September 15, 2014
1. Butteries. Alice, Bob, and Charlotte are looking for butteries. They look in three
separate parts of a eld, so that their probabilities of succes
STAT/MA 41600
In-Class Problem Set #8: September 12, 2014
Solutions by Mark Daniel Ward
1. The mass of X is pX (x) = (32/52)x1 (20/52), for integers x 1. So the CDF of X, for
x
an integer x 1, is FX (
STAT/MA 41600
In-Class Problem Set #8: September 12, 2014
1. Suppose that we choose cards from a standard 52-card deck, with replacement and
shuing in between cards, until the rst card with value 6, 7
STAT/MA 41600
Practice Problems: September 12, 2014
Solutions by Mark Daniel Ward
1. Butteries. Alice, Bob, and Charlotte are looking for butteries. They look in three
separate parts of a eld, so that
STAT/MA 41600
Practice Problems: September 12, 2014
1. Butteries. Alice, Bob, and Charlotte are looking for butteries. They look in three
separate parts of a eld, so that their probabilities of succes
STAT/MA 41600
In-Class Problem Set #7: September 10, 2014
Solutions by Mark Daniel Ward
1. There are 63 = 216 equally-likely possible outcomes. So (1a) we have P (X = 0) =
3
125
25
(1/6)0 (5/6)3 = 216
STAT/MA 41600
In-Class Problem Set #7: September 10, 2014
(there is no Problem Set #6)
1. Roll three (6-sided) dice. Let X denote the number of 2s that appear.
1a. Find P (X = 0). 1b. Find P (X = 1).
STAT/MA 41600
Practice Problems: September 10, 2014
Solutions by Mark Daniel Ward
1. Harmonicas. Since X is a waiting time, then X takes value in the interval [0, ), so X
is a continuous random variab
STAT/MA 41600
Practice Problems: September 10, 2014
1. Harmonicas. When ordering a new box of harmonicas, let X denote the time until the
box arrives, and let Y denote the number of harmonicas that wo
STAT/MA 41600
In-Class Problem Set #5: September 8, 2014
Solutions by Mark Daniel Ward
1. Let A be the event that the random student lives in a residence hall, and let B be the
P (B|A)P (A)
(AB)
event
STAT/MA 41600
In-Class Problem Set #5: September 8, 2014
1. At a certain college, 40% of the students live in a residence hall (on-campus), and the
other 60% of the students live o-campus. Suppose tha
STAT/MA 41600
Practice Problems: September 8, 2014
Solutions by Mark Daniel Ward
1. Waking up at random. 1a. Writing A as the event it is a weekday, and B as the event
it is before 8 AM, we have
P (A
STAT/MA 41600
Practice Problems: September 8, 2014
1. Waking up at random.
On each weekday, a student wakes up before 8 AM with probability .65, or after 8 AM
with probability .35.
On each weekend, a
STAT/MA 41600
In-Class Problem Set #4: September 5, 2014
Solutions by Mark Daniel Ward
1. Let A denote the event that the two results are equal; let B denote the event that the
result on the red die i
STAT/MA 41600
In-Class Problem Set #4: September 5, 2014
1. Roll a red die and a green die. Given that the result on the red die is less than or equal
to the result on the green die, nd the probabilit
STAT/MA 41600
Practice Problems: September 5, 2014
Solutions by Mark Daniel Ward
(AB)
1. Choosing a page at random. (a.) We have P (A | B) = P P (B) . Since A B, then
P (A B) = P (A) = 1/1000. Also P
STAT/MA 41600
In-Class Problem Set #3: September 3, 2014
Solutions by Mark Daniel Ward
1. Events A and B are independent. Why? We note P (A) = 4/8 = 1/2 and P (B) = 4/8 =
1/2, and P (A B) = P (cfw_c,
STAT/MA 41600
In-Class Problem Set #3: September 3, 2014
1. Consider a sample space S with eight outcomes, S = cfw_a, b, c, d, e, f, g, h. Suppose
that each outcome is equally likely to appear. Now de
STAT/MA 41600
Practice Problems: September 3, 2014
Solutions by Mark Daniel Ward
1. Choosing a page at random. Yes, the events are independent. We compute
P (A) = 100/1000 = 1/10;
P (B) = 10/1000 = 1/
STAT/MA 41600
Practice Problems: September 3, 2014
1. Choosing a page at random.
A student buys a brand new calculus textbook that has 1000 pages, each numbered with
3 digits, from 000 to 999. She ran
STAT/MA 41600
In-Class Problem Set #1: August 27, 2014
Solutions by Mark Daniel Ward
Problem Set 1 Answers
1a. When building an event that contains outcome a, we have 6 choices to make, each with
two
STAT/MA 41600
In-Class Problem Set #1: August 27, 2014
1. Consider a sample space S with seven outcomes, e.g., S = cfw_a, b, c, d, e, f, g.
(a.) How many events are there, which contain outcome a?
(b.
STAT/MA 41600
Practice Problems: August 27, 2014
Solutions by Mark Daniel Ward
Problem Set 1 Answers
1. Choosing points at random. (a.) The sample space is
S = cfw_(x, y) | 0 x 2, 0 y 2 x.
(b.) The sa
STAT/MA 41600
Practice Problems: August 27, 2014
1. Choosing points at random.
(a.) A point is chosen at random inside in the triangle in Figure 1. What is the sample
space? [Please give mathematical
STAT/MA 41600
In-Class Problem Set #2: August 29, 2014
Solutions by Mark Daniel Ward
1a. Let Aj denote the event that the jth die has value 2. Then P (A1 A2 A3 ) =
P (A1 ) + P (A2 ) + P (A3 ) P (A1 A2
STAT/MA 41600
In-Class Problem Set #2: August 29, 2014
1. Roll three (6-sided) dice.
1a. Use inclusion-exclusion to nd the probability that at least one value of 2 appears.
1b. Find the probability th