1. 6.4 Find Probabilities of Compound Events
MM1D2a - Find the probabilities of mutually
exclusive events.
MM1D2b – Find the probabilities of
dependent events
MM1D2c – Calculate conditional probabilities

2. Compound Event
Combines two or more events, using the word and or the word or.
And involves multiplication
Or involves addition

3. Mutually Exclusive events
Events with no common outcomes.

4. Overlapping Events
Events with at least one common outcome.

5. Independent Events
The occurrence of one event has no effect on the occurrence of the other.

6. Dependent Events
The occurrence of one event affects the occurrence of the other.

7. Conditional Probability
If A & B are dependent events, then the probability that event B will occur given that event A has occurred.

8. Example 1
You randomly choose a card from a standard deck of 52 playing cards.
Find the probability that you will choose a 9 or King
Solution:
Choosing a 9 or King are mutually exclusive events
P(9 or King) = P(9) + P(King) =

9. Example 1
b) Find the probability that you will choose an Ace or a spade.
Solution
Because there is an Ace of Spades, choosing an Ace or a spade are _____________. There are 4 Aces, 13 spades, and 1 Ace of spades.
P(Ace or spade) = P(Ace) + P(spade) – P(Ace and spade) =

10. Example 2
You roll two number cubes. What is the probability that you roll a 1 first and an 2 second?
Solution
The events are ____________. The number on one number cube does not affect the other.
P(1 & 2) = ______ ∙________ = ______ ∙ ______ = ______

11. Example 3
Markers A box contains 8 red markers and 3 blue markers. You choose one marker at random, do not replace it, then choose a second marker at random. What is the probability that both markers are blue?
Solution
Because you do not replace the first marker, the events are ____________. Before you choose a marker, there are 11 markers, 3 of them are blue. After you choose a blue marker, there are 10 markers left and two of them are blue. So, the ________________ that the second marker is blue given that the first marker is blue is _____.
P(blue and then blue) = ___________ ∙ _________________
= _________ ∙ ___________ = ________________

12. You Try!
In a standard deck of cards, find the probability you will randomly select the King of diamonds or any spade.
In Example 3, suppose there are also 4 orange markers in the box. Calculate the probability of selecting a blue marker and then an orange marker without replacement.