Math 12
Unit 5 - Probability
Day 3 Notes
Probability of Mutually Exclusive Events
Activity #1: The Monty Hall Problem
The Monty Hall problem involves a classical game show situation and is named after
Monty Hall, the long-time host of the TV game show Let's Make a Deal. There are three
doors labeled 1, 2, and 3. A car is behind one of the doors, while goats are behind the other
two:
What is the probability that you choose the car?
As you have already guess it in the title of the notes, the Principle of Inclusion and
Exclusion can be applied to probabilities.
What does it mean to say inclusive? Exclusive?
Draw a Venn diagram of two events that are mutually exclusive.
Draw a Venn diagram of two non-mutually exclusive events.
Example #1:
A card is chosen at random from a pack of 52 playing cards. What is the probability of a
King or a Heart?
Matty 2012
Math 12
Unit 5 - Probability
Day 3 Notes
Example #2:
A number is chosen at random from the set of two-digit numbers from 10 to 99 inclusive.
What is the probability the number contains at least one digit 2?
Example #3:
There are 30 children in a class and they all have at least one cat or
dog. 14 children have a cat, 19 children have a dog.
What is the probability that a child chosen at random from the
class has both a cat and a dog?
Example #4:
A car manufacturer keeps a database of all the cars that are available for sale at all the
dealerships in Western Canada. For model A, the database reports that 43% have heated
leather seats, 36% have a sunroof, and 49% have neither. Determine the probability of a
model A car at a dealership having both heated seats and a sunroof.
Matty 2012
Math 12
Unit 5 - Probability
Day 3 Notes
The rules are as follows:
1. The player selects a door.
2. The host selects a different door and opens it.
3. The host gives the player the option of switching from her original choice to the
remaining closed door.
4. The door finally selected by the player is opened and she either wins or loses.
Suppose you're on a game show, and you're given a choice of three doors. Behind one door
is a car; behind the others, goats. You pick a door--say No. 1--and the host, who knows
what's behind the doors, opens another door--say No. 3--which has a goat. He then says to
you, 'Do you want to pick door No. 2?' Is it to your advantage to switch your choice?
http://www.math.ucsd.edu/~crypto/Monty/monty.html
http://www.math.ucsd.edu/~crypto/Monty/montydoesnotknow.html
Matty 2012