# Let A and B be two events. Fin

Let A and B be two events. Find the largest and smallestpossible values P(A U B) can take in terms of P(A) and P(B) andgive 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 anevent

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

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