an experiment results in one of three mutually exclusive eve

an experiment results in one of three mutually exclusive events, A,B,C. it is known that p(A)=.30, p(b)=.55 and p(c)=.15. find each of the following probabilities

P(AUB)

P(AC)

P(A|B)

P(BUC)

Are B and C Independent Events? Explain.

Solution

P(A) = 0.30

P(B) = 0.55

P(C) = 0.15

Since the events are mutually exclusive:

P(A U B) = P(A) + P (B)

and so P (A and B ) = 0

a)

P (A u B) = P (A) + P(B) = 0.30 + 0.55 = 0.85

b)

P(A and C) = 0 [since the events are mutually exclusive, both the events won\'t happen simutaeously]

c)

P(A|B) = P(A and B) / P(B)

Since, P(A and B) = 0,

P(A|B) = 0

d)

P (B u C) = P(B) + P (C)

= 0.55 + 0.15

= 0.70

The events are dependent as the occurence of one ensures that others don\'t occur for sure. Thus, B and C are dependent.