MB0040 -Q2. State the addition and multiplication rules of probability giving an example of each case.

Solutions: Addition and multiplication rules of probability :

The addition rule of probability:

Case 1: When the event are not mutually exclusive:

i) If ‘A’ and ‘B’ are any two events then the probability of the occurrence of either ‘A’ or ‘B’ is given by:  Ρ(Α ÈΒ)=Ρ(Α)+Ρ(Β)-Ρ(Α ÇΒ)

E.g: The Probability of drawing either a spade or an ace from a well shuffled pack of cards in an example where addition rule of probabilities applies.

A bolt is drawn at random and is found to be defective

Case 2: When the event are mutually exclusive:

ii) If ‘A’ and ‘B’ are two mutually exclusive events then the probability of

occurrence of either ‘A’ or ‘B’ is given by:

Ρ(Α ÈΒ) = Ρ(Α)+Ρ(Β)

e.g: the probability of getting a sum of five 5 or 6 in a single throw with two dice, is an example where the events are mutually exclusive and addition rule of probability applies.

iii) If ‘A’, ‘B’ and ‘C’ are any three events then the probability of occurrence

of either ‘A’ or ‘B’ or ‘C’ is given by:

Ρ(Α ÈΒ ÈC)=Ρ(Α)+Ρ(Β)+Ρ(C) -Ρ(Α ÇΒ) -Ρ(Β ÇC) -Ρ(Α ÇC)+Ρ(Α ÇΒ ÇC)

Multiplication rule

If ‘A’ and ‘B’ are two independent events then the probability of occurrence of ‘A’ and ‘B’ is given by: Ρ(Α ÇΒ)=Ρ(Α)Ρ(Β)

e.g: An urn contains 5 balls- 3 white and 2 black. If two balls are drawn one after another, the probability of both being white, if the first ball drawn is replaced before drawing the second constitute a situation where multiplication rule of probability with independent event is used.