Math 2
7-4 Conditional Probability
 I can calculate conditional probabilities
Name__________________________________
* If events A and B are independent, then P  B | A  P  B  because event A does not affect event B.
* If events A and B are dependent, then you will need to think about how event A happening affects
event B.
Practice 1
You roll a six-sided die and then flip a fair coin. Let A = rolling a 5 or 6 and B = flipping tails
1. P  A  ________
2. P  A | B   ________
3. P  B | A  ________
Practice 2
A poll asked students at a school two questions – (1) where they would like the dance to take place, and (2)
what type of band they would like at the dance. The results are in the below table.
Preference for
Band
Hip-Hop
Classic Rock
Preference for Location
Hotel
Rec Center
73
80
55
92
Totals
Totals
1.
How many students preferred a Classic Rock band?
________
2.
How many students preferred the dance take place at a Rec Center?
________
3.
How many total students were part of the poll?
________
4.
Suppose you pick a student at random from this class. Find each of the following probabilities.
Write your answer as both a fraction and as a decimal.
a.
P(prefers hotel) = ______________
c.
P(prefers hotel and prefers hip-hop band) = ______________
d.
P(prefers hotel | prefers hip-hop band) = ______________
e.
P(prefers hip-hop band | prefers hotel) = ______________
f.
Are the two events prefers hip-hop band and prefers hotel independent? Explain based on your
answers to parts a-e.
Practice 3
b.
P(prefers hip-hop band) = ______________
Practice 4
Consider the data to the right, taken from a math class.
Suppose you pick a student at random from this class.
Let:
Not Wearing
Tennis Shoes
Tennis Shoes
A = wearing tennis shoes
Boy
5
9
B = not wearing tennis shoes
C = Boy
D = Girl
Girl
10
18
1. P(A) = _______
5.
Wearing
2. P(D) = _______
3. P(A | D) = __________
4. P(A and D) = __________
Are the events wearing tennis shoes and is a girl independent? Use your work in problems 1-3 to
explain.
6. P(D | A) = ________ 7. P(B | C) = ________
Further examples:
8. P(C | A) = ________
9. P(B and C) = _______
Practice 5
1.
2.
3.