1. Addition and Multiplication Rules of Probability
Skill 16

2. Objectives
Understand the difference between addition and multiplication rules.
Apply the addition and multiplication rules of probability.

3. P(A or B) = P(A) + P(B) – P(A ∩ B)
General Addition Rule
P(A or B) = P(A) + P(B) – P(A ∩ B)
When to Apply the Addition Rule
Any outcome in A
Any outcome in B
Any outcome in Both A and B

4. Example-Addition Rule
An ice cream cup has 3 scoops of chocolate, 4 scoops of vanilla, and 3 scoops of butter scotch ice cream. What is the probability that if you randomly sampled the ice cream you will taste chocolate or vanilla?
Solution:
P(C ∪ V) = P(C) + P(V) – P(C ∩ V)
P(C ∪ V) = 3/10 + 4/10 - 0
P(C ∪ V) = 7/10

5. Example-Addition Rule
A single standard die is rolled. What is the probability of rolling a six or a one?
Solution:
P(6 ∪ 1) = P(6) + P(1) – P(6 ∩ 1)
P(6 ∪ 1) = 1/6 + 1/6 – 0
P(6 ∪ 1) = 2/6
P(6 ∪ 1) = 1/3

6. Example-Addition Rule
Robert is playing cards. What is the probability of pulling a king or a jack?
Solution:
P(K ∪ J) = P(K) + P(J) – P(K ∩ J)
P(K ∪ J) = 4/52 + 4/52 – 0
P(K ∪ J) = 8/52
P(K ∪ J) = 2/13

7. Example-Addition Rule
Mary is playing cards. What is the probability of randomly pulling a heart or a club out of the deck?
Solution:
P(H ∪ C) = P(H) + P(C) – P(H ∩ J)
P(H ∪ C) = 13/ /52 – 0
P(H ∪ C) = 26/52
P(H ∪ C) = 1/2

8. General Multiplication Rule
P(A and B) = P(A) x P(B)
When to Apply the Multiplication Rule
To find the intersection of A and B
If dependent, P(B) becomes P(B | A)
This is read, Probability of B given A has already happened

9. Example-Multiplication Rule
Christy has a bag of candies. In the bag there are 5 red colors, 3 orange colors and 8 green colors. She takes one candy, records its color and puts it back in the bag. She then draws another candy. What is the probability of taking out a green candy followed by a red candy?
Solution:
P(G ∩ R) = P(G) * P(R, given G)
P(G ∩ R) = 8/16 * 5/16
P(G ∩ R) = 40/256
P(G ∩ R) = 5/32

10. Example-Multiplication Rule
Dena has a box with 7 blue marbles and 3 pink marbles. Two marbles are drawn without replacement from the box. What is the probability that both of the marbles are blue?
Solution:
P(B ∩ B) = P(B) * P(B | B)
P(B ∩ B) = (7/10) * (6/9)
P(B ∩ B) = 42/90
P(B ∩ B) = 7/15

11. Example-Multiplication Rule
John is going to draw two cards from standard deck. What is the probability that the first card is a queen and the second card is a jack?
Solution:
P(Q ∩ J) = P(Q) * P(J | Q)
P(Q ∩ J) = (4/52) * (4/51)
P(Q ∩ J) = 16/2652
P(Q ∩ J) = 4/663 or 0.006

12. Example-Multiplication Rule
Emily has a folder of colored paper. The folder has 4 yellow color papers, 5 black color papers, 6 white color papers, and 5 brown color papers. She picks one paper, record its color, puts it back in the folder and draws another paper. What is the probability of taking out a brown paper followed by a yellow paper?
Solution:
P(B ∩ Y) = P(B) * P(Y | B)
P(B ∩ Y) = (4/10) * (4/9)
P(B ∩ Y) = 20/400
P(B ∩ Y) = 1/20

13. 16: Addition and Multiplication Rules of Probability
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