5.2 Probability continued Flashcards
What is an event?
A specific set of outcomes. Example: rolling an even number, choosing a male, choosing someone who can taco tongue given that they can evil eyebrow.
How do you show something is a valid probability model?
- Note that all the probabilities are between 0 and 1. 2. Show that they all sum to 1.
What does mutually exclusive mean? How do you tell if two events are mutually exclusive?
They can’t happen together. Is P (A and B) = 0?
What does independent mean? How do you tell if two events are independent?
The events don’t affect each other. Therefore, P(A) and P(A given B) and P(A given B complement) should all match. P(B) should also match P(B|A) and P(B| not A)
Can two events be mutually exclusive and independent?
NO!!!! Independent events always “happen” together, they just don’t affect each other. In symbols, Since P(A and B) = 0 for mutually exclusive events, P(A|B) = 0 too. Which means it can’t equal P(A).
When would you multiply probabilities together?
When two events happen together or after each other. So P(A and B) = P(A) * P(B|A). Make sure to adjust the second probably if the events are not independent. This is what a tree diagram does. So if the probability of getting one red marble is 7/10, the probability of getting two (without replacement) is 7/10 * 6/9.
When would you add probabilities together?
When an event is made up of several different outcomes. The most common is an OR statement. Just make sure to subtract any overlap. Another common scenario is when you need to combine multiple branches of a tree diagram (ex: because there is more than one way for the roadrunner to get caught).
When would you want to raise a percent to a power (of n)?
When you want that thing to happen n times in a row. This assumes that each time is independent.
If you know the percent of a success, how do you find P(fail)?
1 - P(success)
How do you find the probability of something happening at least once?
Find the probability of it never happening (P(fail)^n) and then do 1 minus that. Ex: P(getting at least one head in 6 flips) = 1 - P(all tails) = 1 - (.5)^6
If you add up all the numbers in a two-way table or all the individual numbers in a Venn Diagram what should you get?
The total number of outcomes/subjects. So if your venn diagram adds up to too many, you probably didn’t subtract the overlap from each circle.
How do you find P(A and B) in a two-way table?
Just look for the single box where they overlap (or add a couple boxes in special circumstances) and divide by the total total.
How do you find P(A|B) in a two-way table?
Divide the box where they overlap by either the Row or Column total for event B instead of the total total.
How do you change a percent to a decimal?
Move the decimal left 2 (inserting zeros as needed). 3% is 0.03, not 0.3. Be careful!
