Conditional Probability Worksheet
Recall the formula: P ( A | B )
=
P ( A
∩
B )
P ( B )
1) If you roll a fair die twice and observe the numbers that face up, find the probability that the sum of the numbers is 8 given that the first number is 3.
2) Suppose past records in a large city produced the following data on a driver being in an accident on a day when there was record
− breaking rain levels in Seattle.
Accident A No Accident A
C
Totals
Rain R 0.025
No Rain R
C
0.015
Totals .040
0.335
0.625
0.960
0.360
0.64
1.000
A. Find the probability of an accident, rain or no rain.
B. Find the probability of rain, accident or no accident.
C. Find the probability of an accident and rain.
D. Find the probability of an accident, given rain. Be careful here! It’s not the same as C.
3) The table below shows a survey of 100 authors by a publishing company:
New Author (N) Established Author (N
C
) Total
Successful (S)
Unsuccessful (S
C
)
5
15
25
55
30
70
Total 20 80 100
A. Find the probability that an author is established given that she is successful.
B. Find the probability that an author is successful given that he is established.
C. Make up other more conditional probability that you compute from the table, state it, and then give its value.
4) In your project you will need to compute
P ( Y
∩
T
∩
C | S )
=
P ( Y
In class yesterday, we found that P ( S | Y )
=
| S )
×
P ( T
0 .
439
| S )
×
P ( C
. Verify that
| S )
P ( Y | S )
=
.
071 . (Recall that in our class project, use the fact that P ( T
Y
|
= 7 years of experience.) Once you have ve rified
S )
=
0 .
530 , and P ( C | S )
=
0.522 to compute P ( Y
P ( Y
∩
T
| S )
∩
C
=
|
.
071
S ) .
, then
In a complete sentence, explain what your result means.
5) Now compute P ( Y
∩
T
∩
C | S ) for your team’s project data. Hint: If you have completed the list of counts that was requested yesterday, then this should be easy to do and should not require any further Excel work. Check with the instructor to see if your result is correct. If you finish early, also compute P ( Y
∩
T
∩
C | F ) . Doing so will get you close to being done with Parts 3 and 4 of the Project.