Probability and Addition Law Chapter 4 Q30 (adapted)

Link to Youtube

Suppose we have two events, A and B with P(A)=0.50 and P(B)=0.60 and P(AnB)=0.40. (Sorry...the n means intersection)

a. Find P(AUB). This is the union of A and B, or the probability that a sample point is in A or B or both. Use the Addition Law, to give P(AUB) = P(A)+P(B)-P(AnB = 0.50+0.60-0.40=0.70.

b. Find P(A|B) this is P(A) given P(B). The sample space is P(B). Use the formula so P(A|B) = P(AnB)/P(B)
= 0.40/0.60=0.67.

c. Are A and B independent (this is a good question!). If they were independent, then it would be true that
P(A|B)=P(A). In other words, whatever happens to B doesn't affect A. Let's check: is this true?

We know that P(A|B)=0.67. We know that P(A)=0.50. Are they the same? No! So A and B aren't independent. 

d. Now, draw a Venn diagram yourself. You'll have two circles, one for each event. Is there are intersection? What is the probability of that intersection? What is the complement of the union?