If necessary consult a list of formulas a b Clear Let and be

(If necessary, consult a list of formulas.)

(a)

(b)

Clear

Let and be two events such that and . (a) Determine , given that and are mutually exclusive . (b) Determine , given that and are independent . Do not round your responses. (If necessary, consult a list of formulas.)

Solution

a) Mutually exclusive:

P(A B) = 0 and so the addition law becomes P(A U B) = P(A) + P(B)

P(M U N) = P(M) +P(N) = 0.17 + 0.06 = 0.23

b) If A and B are independent, then

P(A B) = P(A)P(B)

So, P( M N) = P(M)*P(N) = 0.17*0.06 =0.0102

So, P(M U N) = P(M) +P(N) - P( M N)

= 0.17 +0.06 - 0.0102

= 0.2198