The Laws of Probability
Notes # ______________
Basic Probability
Probability ____________________________
Complement _____________________________
Notation
Notation
_____________
_______________
If the probability of rolling a ‘2’ on a six sided die is one sixth, what’s the probability of not rolling a 2?
Disjoint or Mutually Exclusive Events
Two events A and B are disjoint or mutually exclusive if ___________________________________________
In algebra: _____________________________________ or _______________________________________
1) A cooler contains 20 bottles made up of 8 cokes, 5 pepsi’s, and 7 waters. The probability of choosing
a coke or pepsi is:
2) For the junior class picnic, parents prepare hotdogs, hamburgers, or bar – b – que sandwiches. They
have 100 hot dogs, 55 hamburgers, and 90 Bar – b – que sandwiches. What is the probability that
you will get a hamburger or a bar – b – que sandwich?
General Addition Law of Probability
The Addition Law of Probability is: ____________________________________________ ; which is used
when two events _____________________________________.
1) In a class there are 12 boys made up of 8 senior and 4 juniors. There are also 8 girls, made up of 3
seniors and 5 juniors. Find the probability of choosing a boy or a senior.
2) In a class there are 12 boys made up of 8 senior and 4 juniors. There are also 8 girls, made up of 3
seniors and 5 juniors. Find the probability of choosing a girl or a junior.
Boy
Girl
Total
Senior
8
3
11
Junior
4
5
9
Total
12
8
20
The Laws of Probability
Notes # ______________
Using the Addition Rule of Probability:
1.
A rental car lot has 49 American made cars and 26 Foreign cars. Of the American cars, 35 of them
are white and of the foreign cars, 15 are white. A car is chosen at random. Find the probability that
the car is American or White.
2.
A rental car lot has 49 American made cars and 26 Foreign cars. Of the American cars, 35 of them
are white and of the foreign cars, 15 are white. A car is chosen at random. Find the probability that
the car is Foreign or not White.
3. A pizza shop has two sizes of pizzas, large and small. On a certain day, a pizza shop made 59 plain
pizza and 72 pizzas with toppings. Of the 59 plain pizzas, 19 were small and of the 72 pizzas with
toppings, 42 were large. A pizza is chosen at random. Find the probability that the pizza is small or
plain.
4.
A pizza shop has two sizes of pizzas, large and small. On a certain day, a pizza shop made 59 plain
pizza and 72 pizzas with toppings. Of the 59 plain pizzas, 19 were small and of the 72 pizzas with
toppings, 42 were large. A pizza is chosen at random. Find the probability that the pizza is large or
with toppings.
The Laws of Probability
Notes # ______________
Independent Events
Two events are independent if knowing one occurs doesn’t change the probability of the other occurring.
 Using the previous example, are choosing a senior and choosing a boy independent?
 If so, P(senior) ∙ P(Boy) = P(Senior boy)
____________________________ =? ___________________________
At Parkland High School, there are 13 math teachers. There are 5 men and 9 women. Of the 5 men, 2 have
their national board certification and of the 9 women 1 has her national board certification. Is choosing a
teacher with national board certification and a woman independent?
Conditional Probability
Definition: ____________________________________________________________________
Notation: _____________________________________________________________________
Boy
Girl
Total
Senior
8
3
11
Junior
4
5
9
Total
12
8
20
Find P(Boy|Senior) – the probability of choosing a Boy given that we chose a senior.
There are 11 seniors and 8 of them are boys, so P(B|S) =
Find P(Senior|Boy) – the probability of choosing a senior, given that we chose a boy.
There are 12 boys, and of those 12, 8 are seniors, so P(S|B) =
P(A  B)
P(A)
P(Senior Boy)
P(Boy | Senior) 
P(Senior)
P(Senior Boy)
P(Senior | Boy) 
P(Boy)
P(B | A) 
You Do:
Find the P(Junior|Girl) = ____________
Find the P(Junior|Boy) = ____________
Find the P(Girl|Senior) = ____________
The Laws of Probability
Notes # ______________
Examples of Conditional Probability
1.
Example: Let a pair of fair dice be tossed. Make a sample space of each possible toss.
a) Find the probability that at least one of the die is a four. _______________
b) Find the probability that the sum is a 7. ________________
c) Find P(the one of the die is a 4|sum is 7). ________________
d) Given that at least one of the dice is 4, find the probability that the sum is 7. ______________
e) Are rolling two dice with at least one of them a 4 and the sum being 7 a) mutually exclusive or
b) independent. Why?
2. A cooler has 12 Coke’s and 15 Pepsi’s. 9 of the Cokes are diet Coke’s and 5 of the Pepsi’s are diet
Pepsi’s. Make a chart of what is in the cooler and find the probability that the bottle is a Coke, given that
the bottle is a diet drink.
3. A cooler has 12 Coke’s and 15 Pepsi’s. 9 of the Cokes are diet Coke’s and 5 of the Pepsi’s are diet
Pepsi’s. Given that the bottle is a Pepsi, find the probability that the bottle is a Diet Pepsi.
4. Are choosing a regular (non diet) and choosing a diet drink independent, mutually exclusive, or
neither? Why?