Problem 4. A factory has 200 machines. Some of these machines are electrical and

Question

Problem 4. A factory has 200 machines. Some of these machines are electrical and the rest are mechanical. And some of these machines are new and the rest are old. The table below gives the number of machines in each category. Machine Type New Old Electrical 80 40 Mechanical 60 20 a) If we define event A as "electrical machine" and event Bas new machine'" determine the values of P(A), P(B), P(AUB), and P(AnB). (2 Points) b) If a machine is picked at random and it turns out to be new, what is the probability that it is c) Are events A and B independent? Explain. (1 Point) electric? (2 Points)

Explanation / Answer

a) P(A) =120/200 =0.6

P(B) =140/200 =0.7

P(AUB) =(80+40+60)/200 =0.9

P(A n B) =80/200 =0.4

b) P(A|B) =P(A n B)/P(B) =0.4/0.7= 0.5714

c) as P(A)*P(B) =0.6*0.7 =0.42 which is not equal to P(AnB) . therefore events A and B are not independent.

electrical mechanical total new 80 60 140 old 40 20 60 total 120 80 200

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