Probability Flashcards
When all outcomes are equally likely
P(event) = number of outcomes in which event occurs/ total number of outcomes
E.g. Even dice
Outcomes 123456
Even outcomes/total no. outcomes
3/6=1/2
When possible outcomes are not equally as likely (relative frequency approach )
P (event )- number of times event occurs / total number of times
80.000 chips made by a machine last year
80 were defective
P(defective) = 80/80,000=0.001
Simple/compound events
Throw a dice
Outcomes : 123456
Event A : outcome 3 (simple)
Event B :outcome 2,4 or 6 (compound)
The probability of a compound event is the sum of the probabilities included
E.g. P(even) =p(2)+p(4)+p(6)
Complementary events
One event is the negation of another
I will be run over by a bus tomorrow, I will not be run over by a bus tomorrow
If events are p(A)+ p(not A) = 1
Equivalently- p(not A) = 1-p(A)
Combining events
A and B - middle Venn diagram
A or B ( A or B or both )
P(A or B) = p(A) + p(B)- p(A and B)
Mutually exclusive events
When two or more events cannot both occur they are mutually exclusive
P(A and B)=0
Venn: separate non touching circles
E.g. A: person is over 60
B: person under 18
P(A or B) = P(A) + P(B)
Conditional probability
Takes into account additional info
E.g. 6 men and 4 women apply for a job including Mary
Nothing is known about any of them so Mary has 0.1% chance
A woman is successful
Prob is now 1/4-0.25%
We write this as p(success|woman)=0.25
“Probability of success given that a woman is successful “
Calculating conditional probabilities
P(A|B)
B has occurred (after the | )
Probability of A looking at B only
P(A|B)= p(A and B)/ P(B)
Dependant and independent events
When P(A) doesn’t equal P(A|B) events a and b are dependant
When P=P(A|B) a and b are independent
Joint probability
P(A and B)=P(A) P(B|A)
If events are independent it becomes
P(A and B)= P(A) P(B) (multiply )
Multiple joint probabilities
Independent .
P(A and B and C)= P(A) P(B) P(C)
Dependant
P(A and B and C) = P(A)P(B|A)P(C|B and A)
