Question 2 Suppose A and B are events in a sample space S su

Question 2: Suppose A and B are events in a sample space S, such that P(A) = 0.5, P(B) = 0.6 and

P(A or B or both) = 0.8. Using the Rules of Probability, find the following.

a) P(A and B) Use Rules

b) P(A given B) =) Use Rules

c) P(not A and not B) Use Rules

d) Verify the following are true (or false) : Events A and B are mutually exclusive Use Definition

e) Events A and B are dependent or independent (argue overall __% are A’s and …. Use Definition

P(A) = 0.5, P(B) = 0.6 and

P(A or B or both) = 0.8
a)
P(A or B or both) = P(A)+P(B)-P(A and B)
P(A and B) = 0.5+0.6-0.8 = 0.3

b)
P(A given B) = P(A and B) / P(B) = 0.3/0.6 = 0.5

c)
P(A and B) is not equals to Zero, It is false

d)
P(A and B) = P(A) * P(B) = 0.5*0.6 = 0.3

It is independent events