1. Section 4-6 Probability of Compound Events SPI 53B: Compute the probability of a simple compound event
Objective:
Compute the probability of a simple compound event (both independent and dependent).
Recall
Probability:
how likely something is to occur
must be between 0 and 1
we computed one simple event
Vocabulary
Independent events:
events that do not influence one another
Dependent events:
events that influence each other

2. Independent Events
Events that do not influence one another
like rolling a red and black number cube
Selecting with replacement
Written as: P(A and B) = P(A) ∙ P(B)
“And” means to multiply
Suppose you roll a red cube and a black cube. What is the probability that you will roll a 3 on the red and an even on the black?
P(roll a 3 on red cube) =
P(roll even on black) =
P(red 3 and black even) =

3. Dependent Events
Events that influence each other
Occurrence of one affects the probability of the other
Written as P(A then B) = P(A) ∙ P(B after A)
In a word game, you choose a tile from a bag containing the letters shown:
A L G E B R A I S C O O L
Without replacing the tile, you select a second tile. What is the probability you will select an A then an L?
1st Selection
2d Selection
There is a total of 13 choices, so…
P(select an A) =
There is a total of 12 tiles for the 2d selection, so …
P(L after A) =
The probability of the
dependent events is:

4. Probability
Suppose you roll 2 cubes. What is the probability that you will roll an odd number on the first cube and a multiple of 3 on the second cube? 3 6 1 2
There are 3 odd numbers out of six numbers.
P(odd) = = 2 6 1 3
P(multiple of 3) = =
There are 2 multiples of 3 out of the 6 numbers.
Is the event dependent or independent?
INDEPENDENT
P(odd and multiple of 3) = P(odd) • P(multiple of 3) 1 2 1 3
= •
Substitute. 1 6 =
Simplify.

5. Probability
Suppose you have 3 quarters and 5 dimes in your pocket. You take out one coin, and then put it back. Then you take out another coin. What is the probability that you take out a dime and then a quarter?
Is the event dependent or independent?
INDEPENDENT
Since you replace the first coin, the events are independent.
P(dime) = 5 8
There are 5 out of 8 coins that are dimes. 3 8
P(quarter) =
There are 3 out of 8 coins that are quarters.
P(dime and quarter) = P(dime) • P(quarter)
= • = 5 8 3 15 64

6. Probability
A teacher must select 2 students for a conference. The teacher randomly picks names from among 3 freshmen, 2 sophomores, 4 juniors, and 4 seniors. What is the probability that a junior and then a senior are chosen?
Is the event dependent or independent?
DEPENDENT
Since you do not replace the first person chosen, the events are dependent. 4 13
P(junior) =
There are 4 juniors among 13 students 4 12
There are 4 seniors among 12 remaining students.
P(senior after junior) =
P(junior then senior) = P(junior) • P(senior after junior) 4 13 4 12 4 39
= • =