This document contains a collection of probability problems and exercises involving concepts like tree diagrams, counting principles, permutations, combinations, and experimental probability. Questions cover topics like calculating probabilities of compound events, arranging books on a shelf, routes on a map, distributions of groups, and passing a multiple choice test by guessing. The document provides explanations, diagrams and multi-step calculations to work through each probability problem.

1. A Probability Workshop
CHANCE by eisenrah

2. HOMEWORK
The probability that Tony will move to Winnipeg is 2/9, and the probability that
he will marry Angelina if he moves to Winnipeg is 9/20. The probability that he
will marry Angelina if he does not move to Winnipeg is 1/20. Draw a tree
diagram to show all outcomes.
1. What is the probability that Tony will move to Winnipeg and marry
Angelina?
2. What is the probability that Tony does not move to Winnipeg but does
marry Angelina?

3. 3. What is the probability that
Tony does not move to Winnipeg
and does not marry Angelina?

4. HOMEWORK
(a) How many different 4 digit numbers are there in which all the
digits are different?
(b) If one of these numbers is randomly selected, what is the probability it
is odd?
(c) What is the probability it is divisable by 5?

5. HOMEWORK
An examination consists of thirteen questions. A student must answer only one
of the first two questions and only nine of the remaining ones. How many
choices of questions does the student have?

6. HOMEWORK
Randomly arranged on a bookshelf are 5 thick books, 4 medium-sized books,
and 3 thin books. What is the probability that the books of the same size stay
together?

7. Randomly arranged on a bookshelf are 5 thick books, 4 medium-sized books,
and 3 thin books.
How many ways can the 12 books be arranged on a shelf?
How many ways can books of the same size stay together?
What is the probability that the books of the same size stay together?

8. The Town of Esker
The diagram shows a road
grid in the town of Esker. The
roads are restricted by a river on
one side and a lake on the other.
Anson lives at point A and his
friend Bettina lives at point B.
Anson visits Bettina frequently,
and likes to take a different route
each time.
Anson stays on the roads and travels only south and east. How many routes are
there from:
(a) A to C? (b) C to D? (c) D to B?
(d) A to B? (e) A to B if he must go through point P?
(f) What is the probability that
Anson will go through point P
if all routes are randomly
chosen?

9. Design an experiment using the random number
function of your calculator to determine the
probability of passing a six-question multiple choice
test if you guess all the answers. Each question has
four answers, and one answer is correct in each case.
How many simulations would seem reasonable? What
is the experimental probability of getting at least 50%
on the test?

10. Design an experiment using the random number
function of your calculator to determine the
probability of passing a six-question multiple choice
test if you guess all the answers. Each question has
four answers, and one answer is correct in each case.
How many simulations would seem reasonable? What
is the experimental probability of getting at least 50%
on the test?

11. Design an experiment using the random number
function of your calculator to determine the
probability of passing a six-question multiple choice
test if you guess all the answers. Each question has
four answers, and one answer is correct in each case.
How many simulations would seem reasonable? What
is the experimental probability of getting at least 50%
on the test?

12. While working on a problem, Chris observed and give the same value but
that the value for is larger the the value for . Explain why this outcome
occurs.

13. A party of eight boys and eight girls are going for a picnic. Six of the party can
ride in one car, and four in another. The rest must walk. (Assume anyone can
drive.)
(a) In how many ways can the party be distributed for the trip
(b) What is the probability that no girl will have to walk?
(c) What is the probability that no girl will have to walk if each of the two
boys who owns the cars drives his own car?

14. Fred is in a class that has 7 boys and 15 girls. The teacher selects partners for
a project by drawing names from a hat. What is the probability that Fred's
partner will be a boy?

15. Fred is in a class that has 7 boys and 15 girls. The teacher selects partners for
a project by drawing names from a hat. What is the probability that Fred's
partner will be a boy?

16. If you read this slide and leave a comment on the
blog you can get a bonus mark on the test. We'll call
it a quot;homework mark.quot; I figure if you went through
all the slides and read this you were probably
looking for your homework assignment with the
intention of doing it. Your reward for quot;doing your
homeworkquot; this weekend is that you have no
homework. Your quot;bonus commentquot; has to be made
before 6pm Sunday, March 9. If you're only
checking on the blog after that time, well, next time
get your homework done earlier. Enjoy your
weekend. ;-)