Adding Probabilities

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Probability is a numerical measure of the likelihood that a specific event will occur.

Two properties of probability:-

· The probability of an event always lies in the range 0 to 1.


Whether it is a simple or a compound event, the probability of an event is never less than 0 or greater than 0.

· The sum of the probabilities of all simple events (or final outcomes) for an experiment, is always 1.

     Adding probabilities or addition rule to find the probability of union of events: -

The probability of the union of two events A and B is

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

Thus, to calculate the probability of the union of two events A and B, we add their marginal probabilities and subtract their joint probability from this sum.

 

Example: - If P (A or B)= 0.67 and P(A and B) = 0.57 then find P(A) + P(B).

Solution: - Since

P (A or B) = P(A) +P(B) – P(A and B)
P (A) +P (B) = P (A or B) + P (A and B)
                    = 0.67 + 0.57
                    =1.24

 
Example: -  Given that A and B are two mutually exclusive events,
Find P( A or B) when P(A) = 0.47 and P(B)= 0.32

 Solution: - Since A and B are two mutually exclusive events which mean both A and B cannot occur simultaneous. So their joint probability is zero.

            P (A and B) = 0
P(A or B) = P(A) +P(B) – P(A and B)
            = 0.47 + 0.32–0
                 =0.79
 
 

 

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