# AP Statistics Section 6.3C More Conditional Probability

```AP Statistics Section 6.3C
More Conditional Probability
Recall that the conditional
probability of B, given A, is:
P( B  A)
P( B / A) 
P( A)
Example: Use the table from the last page of notes to determine the
conditional probability that a grade at the university is an A, given that it
comes from a liberal arts course.
L = grade from a liberal arts course
6300
P(L) =
 .63
10000
2142
P(L and A) =
 .2142
10000
.2142
P(A | L) =
 .34
.63
P ( A / L)
The intersection of any collection
of events is the event that ___
all of
the events occur.
The extended multiplication rule
looks like this:
P( A  B  C )  P( A)  P( B / A)  P(C / A  B)
Example: Only 5% of male high school basketball, baseball and
football players go on to play at the college level. Of these, only
1.7% enter major league professional sports. About 40% of the
athletes who compete in college and then reach the pros have a
career of more than 3 years. Define the events as follows:
A = {competes in college} .05
B = {competes professionally given they played in college} .017
C = {pro career longer than 3 years given they played in college
and then went on to the pros} .4
What is the probability that a high school athlete competes in
college and then goes on to have a pro career of more than 3
years?
P( A  B  C )  .05  .017  .4  .00034
Example: Online chat rooms are dominated by
the young. Teens are the biggest users. If we
look only at adult internet users (aged 18 and
older), 47% of the 18 to 29 age group chat, as do
21% of those aged 30 to 49 and just 7% of those
50 and over. To learn what percent of all adult
internet users participate in chat rooms, we also
need the age breakdown of users: 29% of adult
users are aged 18 to 29, 47% are aged 30 to 49
and 24% are 50 and over. We will use a tree
diagram to organize our thinking.
Chat .47
No .53
18  29
.29
.1537
Chat .21
.0987
No .79
.3713
30  49
.47
over 50
.24
.1363
Chat .07
No .93
.0168
.2232
What percent of all adult internet
users take part in chat rooms?
.1363  .0987  .0168  .2518
What percent of adult chat room users are
between 18 and 29 years old?
P(18  29  chat )
P(18  29 / chat ) 
P(chat )
.1363

 .5413
.2518
Are the events “18-29 year old internet user”
and “adult chat room user” independent”?
NO
P(18  29)  P(18  29 / chat )
.29  .5413
```
Biostatistics