Exercises for self study. Complete these exercises in the textbook and
compare your solutions against those in the back of the book. These
exercises will not be graded.
pp. 475, 476, Exercises 17 and 33
pp. 492, 493, Exercises 19 and 25
Exercises to be graded. Complete these exercises and turn in your
solutions.
Let $p$ be a probability on a sample space $\Omega$. Prove that, if $E$
and $F$ are events in $\Omega$ such that $E \subseteq F$, then
$p(E) \le p(F)$.
A five-card poker hand is delt from a standard 52-card deck. Answer the
following questions. Explain how you derived your answers.
(a) What is the probability of getting all five cards in black
(i.e., clubs, spades or both)?
(b) What is the probability of getting all five cards being face
cards (i.e., jack, queen and/or king cards)?
(c) What is the probability of getting a straight (i.e., five cards
of sequential ranks) in black?
(d) What is the probability of getting a full house (i.e., three
cards of one rank and two cards of another rank) in face cards?
An urn has three blue and four gold balls, and three balls are chosen
from the urn at random without replacement. Answer the following questions.
Explain how you derived your answers.
(a) What is the probability of choosing all three balls in blue?
(b) What is the probability of choosing all three balls having the same
color?
(c) What is the probability of choosing one blue and two gold balls?
(d) What is the probability of choosing two blue and one gold balls?
A fair coin is tossed four times. In a sample space $\Omega$ of all 16
outcomes, consider the event $E$ of all outcomes in which at least two
tosses land on heads and the event $F$ of all outcomes in which at least
two tosses land on tails. Are $E$ and $F$ independent? Prove your claim.
Plagiarism and academic dishonesty.
Remember, under any circumstance, you must not copy part or all of another's
work and present it as your own. For more details, read
our course policy on plagiarism and
academic dishonesty.
