In: Statistics and Probability
Let A and B be two events. Find the largest and smallest possible values P(A U B) can take in terms of P(A) and P(B) and give examples in which these values can be attained.
From Set Theory we know
For P(AUB) to be the largest
So that P(AUB)= P(A) +P (B)
As there is no intersection between the sets P(AUB)= P(A)+P(B0
For example if P(A)=0.6 and P(B)=0.4 and then P(AUB)=1which is the maximum value for probability of an event
For P(AUB) to be smallest
If P(A) > P(B)
then
and P(AUB)=P(B)
For example
If P(A)=0.6 and P(B)=0.4 and
Then P(AUB)= 0.6+0.4-0.6=0.4 this will be the smallest value