Probability and Statistics Tree Diagram Quiz

P(A|B)

P(AnB)/P(B)

P(AuB)

P(A)+P(B)-P(AnB)

General Multiplication Rule

(does not require independent terms)

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

How to find whether events are independent

P(A)=P(A|B) or P(B)=P(B|A)

General Multiplication Rule if A and B are independent

P(AnB)=P(A)*P(B)

General Addition Rule

P(AuB)=P(A)+P(B)-P(AnB)

Independence

outcome of one event does not influence the probability of the other

Are disjoint events independent

no - one occurring means the other didn’t

Does conditional probability require independence?

no!

How do you solve ordered probability?

2*P(A)*P(B)

more specifically P(A then B) + P(B then A)

Disjoint?

P(AnB)=0

What is the inverse of P(at least one)

P(none)

so P(at least one)=1-P(none)

A^C

everything except all of A

A

all of set A

AuB

all of both sets

AnB

Everything that is in BOTH sets

A^C u B

everything except stuff solely A

A^C u B^C

everything except AnB

A^C n B

only B

A^C n B^C

everything outside of both