Download Notes 12.4 The Multiplication Rule.notebook

Notes 12.4 The Multiplication Rule.notebook
March 30, 2015
Notes 12.4: The Multiplication Rule
In lesson 12.3 we discussed "or" questions. Today, let's look at "and" questions!
Or Probability vs. And Probability • typically involve 1 trial • mutually exclusive vs. not mutually exclusive
• Use addition within the formula to solve
• Increases probability
• typically involve 2 or more trials • independent vs. dependent
• P(A|B) or P(B|A)
• Use multiplication within the formula to solve
• Decreases probability
Notes 12.4 The Multiplication Rule.notebook
March 30, 2015
Let's start by looking at the fancy notation!
General Multiplication Rule: [on reference sheet]
P (A and B) = P(A) * P(B l A)
probability of A
probability of B given A (odds B happens as long as A happens)
P (A and B) = P(B) * P(A l B)
probability of B
probability of A given B (odds A happens as long as B happens)
Notes 12.4 The Multiplication Rule.notebook
March 30, 2015
1. Given the set: A, B, C, D, E, F, G, H, I, J, K
a. What is the probability of randomly selecting a letter that is both a consonant and black?
P(constant and black) = P(constant) * P(black Ι constant) =
b. What is the probability of randomly selecting a letter that is a consonant or black?
P(consonant or black) = P(consonant) + P(black) ­ P(consonant and black) = Notes 12.4 The Multiplication Rule.notebook
2. Mr. Pample has 36 students in his Algebra 2 class. 75% of those students are female. 88.9% of the students are passing given that they are females. 72.7% of the students are female given that they are a passing student. What is the probability of randomly selecting a student from Mr. Pample's class who is female and who is passing?
P (F and P) = P(F) * P(P l F)
P (P and F) = P(P) * P(F l P)
March 30, 2015
Notes 12.4 The Multiplication Rule.notebook
March 30, 2015
Just like with the addition rule, there are instances where the multiplication rule can be easier based on the type of problem you have. Independent events: one event does not impact the other; replacement, two random events, or pure chance
Dependent events: one event does impact the other; no replacement
Notes 12.4 The Multiplication Rule.notebook
March 30, 2015
Determine if the following are independent or dependent events.
3. Using a six­sided die, rolling a 5 and then rolling a 6
4. Selecting a Queen out of a deck of cards and then selecting a Jack out of the same deck
5. Randomly selecting a President and then a Vice­President out of a list of 12 candidates
6. Spinning a spinner with 5 colors and flipping a coin
Notes 12.4 The Multiplication Rule.notebook
March 30, 2015
Why do we care??? You use a different formula depending on whether the events are independent or dependent.
For independent events:
Multiplication Rule: P(A and B) = P(A) * P(B) if A and B [on reference sheet]
For dependent events:
General Multiplication Rule: P (A and B) = P(A) * P(B l A) [on reference sheet]
Notes 12.4 The Multiplication Rule.notebook
Determine if the events are independent or dependent. Then, find the probability.
7. What are the odds of getting a tail on each of 2 coin flips?
A bowl contains 2 black, 3 yellow, and 5 blue marbles. 8. What is the probability that you select a blue marble on the first trial and a yellow marble on the second trial if you do not replace?
9. What is the probability that you select a blue marble on the first trial and a yellow marble on the second trial if you do replace?
10. What are the odds of getting 2 blue marbles if you do not replace?
11. What is the probability of getting 2 blue marbles if you do replace?
March 30, 2015