Stats Unit 3

Probability

Short run is unpredictable

Long run is predictable

Law of Large Numbers

Simulated probabilities tend to get closer to the true probability as the number of trials increases

“After many, many [context], the percent of times [context] approaches [probability] in the long run.”

Probability Sentence

Probability is unpredictable in the short run and streaks are common.

Is probability predictable or not?

Simulation

A way to model random events such that simulated outcomes closely match real world outcomes

Evidence for a claim

Assuming a claim is true, find the true probability of getting the deserved result or more extreme

• <5%; statistically significant, convincing evidence against the claim

Probability of gettingC more/less than a result in however many simulated trials.

Where does the percentage you compare to the <5% statistically significant come from?

Complement Rule Notation

P(A^C)= 1- P(A)

Complement Rule

Probability of an event not happening

Probability of event A and B happening notation

P(A∩B)

Probability of event A and B happening

Multiply Probabilities

Probability of event A or B happening notation

P(A∪B)

Probability of event A or B happening

Add Probabilities

Mutually Exclusive

two or more outcomes that cannot happen at the same time

Addition Rule Notation

P (A or B) = P(A) + P(B) - P(A and B)

Addition Rule

When two events can happen at the same time (they are not mutually exclusive or are overlapping), you must account for their intersection so you do not count the overlap twice

• Drawing a heart or a face card from a deck (there is overlap by 3 cards)

Check if the conditional probability of one event stays the same given whether or not the other event occurs

How can you tell from a two-way table if two events are independent

Conditional Probability Notation

P (A|B) = P(A and B)/ P(B)

Independent Events

Knowing whether or not one event occurs does not change the probability of the other event.

• If P(A)= P(A|B) = P(A/B^c)

With Replacement means the events are _____

Independent

General Multiplication Rule Notation

P(A and B) = P(A) * P(B|A)

General Multiplication Rule

finds the probability that two events, A and B, both happen at the same time using the formula

• Used in tree diagrams

• P(A) is the first event happening and P(B|A) is the conditional probability given A occured

Tree Diagrams