Download 4-6 PPT Probability Compound Events

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).
Probability:
• how likely something is to occur
• must be between 0 and 1
• we computed one simple event
Independent events:
• events that do not influence one another
Dependent events:
• events that influence each other
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?
1
3 1
P(roll a 3 on red cube) =
P(roll even on black) = 
6
6 2
1
1
1
P(red 3 and black even) =  
6 2 12
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…
2
P(select an A) = 13
The probability of the
dependent events is:
There is a total of 12 tiles for
the 2d selection, so … 2 1

P(L after A) =
12 6
2 1 1
 
13 6 39
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?
P(odd) = 3 = 1
6 2
P(multiple of 3) = 2 = 1
6 3
There are 3 odd numbers
out of six numbers.
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•1
Substitute.
2 3
=1
Simplify.
6
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
P(quarter) = 3
8
There are 5 out of 8 coins that are dimes.
There are 3 out of 8 coins that are
quarters.
P(dime and quarter) = P(dime) • P(quarter)
15
5 3
= 8 • 8 = 64
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
P(junior) =
There are 4 juniors among 13 students
13
There are 4 seniors among 12
P(senior after junior) = 4
remaining students.
12
P(junior then senior) = P(junior) • P(senior after junior)
4 4
4
= 13 •12 =
39