More on independence and dependence, discussion of mutually exclusive events.

1. Risk is when an
outcome’s probability
is known. Uncertainty
is when an outcome’s
probability is
unknown.

2. `
Phone Numbers
A computer is used to generate random telephone numbers. Of the
numbers generated and in service, 56 are unlisted and 144 are listed
in the telephone directory. If one of these telephone numbers is
randomly selected, what is the probability that it is unlisted?

3. The probability that Gallant Fox will win the first race is 2/5 and that
Nashau will win the second race is 1/3.
1. What is the probability that both horses will win their
respective races?
2. What is the probability that both horses will lose their
respective races?
3. What is the probability that at least one horse will win a race?

4. Chad has arranged to meet his girlfriend, Stephanie, either in the
library or in the student lounge. The probability that he meets her
in the lounge is 1/3, and the probability that he meets her in the
library is 2/9.
a. What is the probability that he meets her in the library or
lounge?
b. What is the probability that he does not meet her at all?

6. Mutually Exclusive Events ...
Two events are mutually exclusive (or disjoint) if it is impossible for
them to occur together.
Formally, two events A and B are mutually exclusive
if and only if
Not Mutually Exclusive
Mutually Exclusive
Examples:
1. Experiment: Rolling a die once
Sample space S = {1,2,3,4,5,6}
Events A = 'observe an odd number' = {1,3,5}
B = 'observe an even number' = {2,4,6}
A B = (the empty set), so A and B are mutually exclusive.

7. Mutually Exclusive Events ...
Two events are mutually exclusive (or disjoint) if it is impossible for
them to occur together.
Formally, two events A and B are mutually exclusive
if and only if
Not Mutually Exclusive
Mutually Exclusive
Examples:
1. Experiment: Rolling a die once
Sample space S = {1,2,3,4,5,6}
Events A = 'observe an odd number' = {1,3,5}
B = 'observe an even number' = {2,4,6}
A B = (the empty set), so A and B are mutually exclusive.
2. A subject in a study cannot be both male and female, nor can
they be aged 20 and 30. A subject could however be both male
and 20, or both female and 30.

8. Example
Suppose we wish to find the probability of drawing either a king or a spade
in a single draw from a pack of 52 playing cards.
We define the events A = 'draw a king' and B = 'draw a spade'
Since there are 4 kings in the pack and 13 spades, but 1 card is
both a king and a spade, we have:
P(A U B) = P(A) + P(B) - P(A B)
= 4/52 + 13/52 - 1/52
= 16/52
So, the probability of drawing either a king or a spade is 16/52 = 4/13.

9. Identify the events as:
mutually exclusive
dependent
Drag'n Drop
not mutually exclusive
independent
Baby!
a. A bag contains four red and seven black marbles. The event
is randomly selecting a red marble from the bag, returning it to
the bag, and then randomly selecting another red marble from the
bag.
mutually exclusive
independent
b. One card - a red card or a king - is randomly drawn from a
deck of cards.
not mutually exclusive
independent
c. A class president and a class treasurer are randomly
selected from a group of 16 students.
mutually exclusive
dependent
d. One card - a red king or a black queen - is randomly drawn
from a deck of cards. mutually exclusive
independent
e. Rolling two dice and getting an even sum or a double.