STAT 371 Assignment 3 solutions
1. A standard deck of cards is randomly divided into 4 piles of 13 cards each. What is
the chance that each pile contains an ace?
Solution 1: We can use inclusion-exclusion. For 1 i 4, dene Ai to be the event
that the ith p
STAT 371 Term Exam II solutions
1. The diagram shows the h-function for a random walk on a graph with two values
missing. Calculate h(x) and h(y). Hint: Both of the unknown values are fractions with
denominator 11".
h(y)
114/11
h(x)
0
65/11
95/11
Solution
STAT 371 Term Exam I solutions
1.
. .
When rolling a fair die, how long on average until you see two sixes . . in a row?
Solution: Let X be the number of rolls needed with no head start, and Z the number of
.
rolls needed with a head start of . . Then we
STAT 371 Term Exam I solutions
1.
. .
When rolling a fair die, how long on average until you see two sixes . . in a row?
Solution: Let X be the number of rolls needed with no head start, and Z the number of
.
rolls needed with a head start of . . Then we
STAT 371 Assignment 5
Due Thursday November 20 in class
1. Roll a fair die until
values have occurred?
2.
.
.
appears for the third time. What is the chance that all six
Roll a fair die until you have either seen all 3 different odd numbers
all 3 differen
STAT 371 Assignment 4 solutions
1. (a)
Albert has three loonies and an unlimited supply of toonies. Write down the counting generating function G(s) =
an sn , where an means the number of ways that
Albert can make change for n dollars. Calculate a10 .
(b)
STAT 371 Term Exam II solutions
1. You roll a fair die until you see the pattern
needed?
. . . On average, how many rolls are
.
Solution: Let e0 and e1 be the expected number of dice rolls needed with a head start of
nothing, and
.
respectively.
First ste
STAT 371 Term Exam I solutions
1.
Take a symmetric random walk on four points arranged in a circle. What is the
average number of steps needed to return to the starting point?
a
d
b
c
Solution: Without loss of generality, let us suppose that the random wa
STAT 371 Assignment 3 solutions
1. There are 30 people; 17 men and 13 women. These people are randomly divided into
ve groups of size six. What is the chance that there is an all-male group?
Solution: Begin with a set of 30 people P = cfw_1, 2, . . . , 30
Name:
STAT 371 Midterm
Student Number:
Exam, Form: A
TA:
Date:
1. (10pts) Find P (1.5 Z < 1.5) if Z N (0, 1).
(a) .933
(b) .067
(c) .866
(d) None of the above.
Questions 2 - 5 refer to the following situation:
The probability that an online survey results
STAT 371 Assignment 1 solutions
1. There are three pairs of gloves; a red pair, a white pair, and a blue pair. Three people
each randomly grab two gloves. Whats the chance that nobody gets a matching pair?
6
Solution: The chance that the rst person does n
STAT 371 Homework Solution 2
(2.2.2)
By choosing the X-axis properly, the dotplot can be drawn like this:
(2.2.6)
The breaks of frequency distribution should be chosen properly. For example, a possible frequency table
can be:
The corresponding histogram i
STAT 371 Assignment 2 solutions
1. A machine throws two dice. If the two dice values are equal then Player A wins, if
they add up to seven then Player B wins, otherwise the players throw the dice again.
What is the probability than Player A will eventuall
STAT 371 Term Exam I solutions
1. Calculate the total number of strings of strictly positive integers that add up to 6.
This includes: (6), (1, 5), (5, 1), . . . , (2, 3, 1), . . . , (1, 1, 1, 1, 1, 1).
Solution: For k from 1 to 6, stars and bars tells us
STAT 371 Term Exam I solutions
1. A dice throwing game consists of several rounds, where players A and B alternately
throw a pair of fair dice. Player A starts with the rst throw. If player A throws a sum
of 7, he wins and the game stops. Otherwise, if pl
STAT 371 Assignment 4 solutions
1. If you roll a fair die ten times, what is the chance that there are at least three consecutive rolls with the same value?
Hint: Instead of rolling ten times and asking "did we observe 3 consecutive values?",
roll until y
STAT 371 Final Exam - 2013 solutions
1. If you write the letters "b a n a n a" in a random order, whats the probability that no
consecutive letters are the same?
Solution: The total number of permutations of these six letters is
6!
3! 2!
= 60.
We nd the n
STAT 371 Assignment 2 solutions
1. The six letters cfw_a, b, c, a, b, c are written in random order. What is the chance that the
pattern abc does not appear on 3 consecutive letters?
Solution: There are 6 permutations where the rst three letters are abc.
STAT 371 Assignment 5 solutions
1. What is the chance that at least two out of 23 randomly selected people have the same
birthday?
On Mars, where the year has 687 days.
On Venus, where the year has 225 days.
Solution: If there are r days in a year then
STAT 371 Assignment 1 solutions
1. Three friends independently use Quick Pick to randomly select six Lotto 6-49 numbers
from the set cfw_1, 2, . . . , 49. What is the chance that they have at least one number in common
on their tickets?
Solution: Let X, Y
STAT 371 Assignment 1 solutions
1. Here is a random experiment: toss a fair coin and count the number of trials until the
third head appears. Since the total probability adds up to one, deduce that
k=2
k
1
= 1.
k+1
2 2
Solution: There are k strings of len