Let A and B be two events. Find the largest and smallest possible values P(A U...

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.

Solutions

Expert Solution

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

orchestra answered 1 year ago

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