Unit 6, Modeling with Probability
Name _____________________________
Practice 6-6, Independence & Conditional Probability
Date ____________ Period ___________
Recall that two events are independent when ______________________________________________.
This is usually easy to determine if we know what the two events are. But how can we check whether two
events are independent if we just know some of the probabilities of the events? There are three simple ways:
1. Is P(A and B) = ___________________ ?
2. Is P(B|A) = _________ ?
3. Is P(A|B) = _________ ?
If you answer yes to any one of these three questions then events A and B are _________________________.
Also, you only need to verify that _______ of them is true; if ________ is true, then ____________________.
Note that the Multiplication Rule (___________________________________) is a formula that can be used to
determine the value of _________, _________, or _____________. If you know two of these values, you can
determine the value of the remaining one.
Note that the Addition Rule (_______________________________________) is a formula that can be used to
determine the value of _________, _________, ___________, or _____________. If you know three of these
values, you can determine the value of the remaining one.
Events A and B are independent. Find the indicated probability.
1. P(A) = 0.3
2. P(A) = _________
P(B) = 0.9
P(B) = 0.3
P(A and B) = _________
P(A and B) = 0.06
3. P(A) = 0.75
P(B) = _______
P(A and B) = 0.15
Events A and B are dependent. Find the indicated probability.
4. P(A) = 0.1
5. P(A) = _______
P(B|A) = 0.8
P(B|A) = 0.5
P(A and B) = _________
P(A and B) = 0.25
6. P(A) = 0.9
P(B|A) = ________
P(A and B) = 0.54
Find the indicated probability. Then determine if events A and B are independent. (Use one of the 3 ways.)
7. P(A) = 0.7
8. P(A) = 0.5
9. P(A) = 0.2
P(B) = 0.2
P(B) = 0.4
P(B) = 0.7
P(A or B) = _____
P(A or B) = 0.9
P(A or B) =
P(A and B) = 0.1
P(A and B) = _____
P (A and B) = .14
Are A and B independent?
Are A and B independent?
Are A and B independent?
Word Problems
10. Mr. B has collected data on his students over the past several years and has calculated the following
probabilities for this course: The probability of a student getting an A is 0.25; the probability of being
female is 0.60; and the probability of getting an A AND being female is .15.
a) Are the two events “getting an A” and “being female” independent events? _____Use one of the 3 ways
above to confirm your answer.
b) Draw a Venn diagram to represent this situation.
c) What is the probability of getting an A or being female?
11. In Mr. Jonas' homeroom, 70% of the students have brown hair, 25% have brown eyes, and 5% have both
brown hair and brown eyes. A student is selected at random. Given that the student has brown hair, what
is the probability that the student also has brown eyes?
12. A survey asked students which types of music they listen to. Out of 200 students, 75 indicated pop
music and 45 indicated country music, with 22 students indicating they listened to both. Use a Venn
diagram to find the probability that a randomly selected student listens to pop music given that they
listen country music.