Download Conditional Probability

Conditional Probability
Conditional Probability
The probability of an event A, given the
occurrence of some other event B:
P  A and B 
P  A B 
P  B
Ex: A card is selected from a standard 52
Given (B)
card deck. If a red card
is
selected,
what
Desired (A)
is the probability it is a King? Want: P  king red 
P king and red 
P red 

2
52
26
52

1
13
Example 1
On the midway at the county fair, there are many
popular games to play. One of them is “Flip to Spin
or Roll.” You start by flipping a coin. If heads
comes up, you get to spin the big wheel, which
has ten equal sectors: three red, three blue, and
four yellow. If the coin shows tails, you get to roll a
cube with three red sides, two yellow sides, and
one blue side. If your spin lands on blue, or if the
blue side of the cube comes up, you win a stuffed
animal.
Suppose that you know that Tyler won a stuffed
animal. Figure out what the probability that he
started off with heads.
Example 1: Area Model
Wheel
COIN
Find the probabilities.
H
1
2
T
1
2
R
3
10
HR
3
20
B
HB
1
4
TR
If you make an area
diagram, it is ok to scale
the lengths differently.
R
1
2
3
10
3
20
TB
B
Y
2
5
HY
1
5
1
12
TY
1
6
Cube
3
P  Heads and Blue
P  heads given that he won  
 3 20 1 
P  Win 
20  12
Y
3
20
7
30
1
6
1
3
 149  64.3%
Example 2
A survey of 500 adults asked about college expenses. The
survey asked questions about whether or not the person
had a child in college and about the cost of attending
college. Results are shown in the table below:
Cost too Much Cost Just Right
Cost Too Low
Child in College
0.30
0.13
0.01
Child not in College
0.20
0.25
0.11
Suppose one person is chosen at random. Given that the
person has a child in college,
college what is the probability that
he or she ranks the cost of attending college as “cost
cost too
too
much”?
much Desired
Want: P "cost too much" "child in college"
P"cost too much" and "child in college"
P"child in college"


0.30
0.30  0.13  0.01
0.30
 0.682
0.44