- P(A')=1-P(A)
- P(Φ)=0
- If A⊆B then P(A)<=P(B)
- P(AUB)=P(A)+P(B)-P(A⋂B)
- P(A|B)=P(A)-P(A⋂B)
Note:
- If A and B are mutually disjointed then A⋂B=Φ, so that P(A⋂B)=P(Φ)=0
- P(AUB) is also written as P(A+B). Thus for mutually disjoint events A & B
- If A,B and C are any three events then P(AUBUC)=P(A)+P(B)+P(C)-P(A⋂B)-P(B⋂C)-P(C⋂B)+P(A⋂B⋂C)
Let S be the sample space of any Random experiment are two associated events with S. Then, the conditional probability of the event E if F has occured is denoted by P(E/F) and given by
P(E/F)=
Q.) An experiment has occured of tossing three coins. What is the probability of event E when F is occured; where E has atleast two head appears and F has it's first coin shows tail.
Q.) A bag contains 10 white and 3 red balls while another bag contains 3 white and 5 red balls. Two balls are drawn at random and put in the second bag. Then a ball is drawn at random from the second bag, what is the probability that it is a white ball?
A.)
=59/130