Assume that Pr[A′]=0.4 , Pr[B]=0.6 , and Pr[A′∩B]=0.3. Find probability of following events:

Question

(1) Pr[A∩B] =

(2) Pr[A∪B] =

(3) Pr[A′∪B] =

Answer 1

It's very useful to draw a Venn diagram for problems like these. Here is an animation I made to illustrate the different probabilities:

https://drive.google.com/file/d/1S9sBcYRZIgvliA9iM3mWy77nCty76GxQ/view?usp=sharing

Go through it slowly and try to apply this method to similar problems. If you need further explanation, please feel free to contact a tutor for a lesson.

Cheers,

Patrick

Answer 2

Pr[A] = 1 - Pr[A'] = 0.6

Next, the events A'∩B and A∩B are disjoint, and (A'∩B) ∪ (A∩B) = B.

Then Pr[A'∩B] + Pr[A∩B] = Pr[B]

So, Pr[A∩B] = 0.6 - 0.3 = 0.3

To find other probabilities, use the General Addition Rule:

Pr[A∪B] = Pr[A] + Pr[B] - Pr[A∩B]

Pr[A'∪B] = Pr[A'] + Pr[B] - Pr[A'∩B]