Suppose that after 10 years of service 40 of computers have

Suppose that after 10 years of service, 40% of computers have problems with motherboards, 30% have problems with hard drives, and 15% have problems with both the motherboard and the hard drive. (a) Are the events A have problems with motherboards\" and B have problems with hard drives independent? Why or why not? (b) What is the probability that after 10 years of service the mother- board of a computer has problems given that its hard drive is in good working order?

Solution

a) P(AnB)=P(A)*P(B) when A and B are independent

P(AnB)=0.5

P(A)*P(B)=0.4*0.3=0.12

so A and B are dependent

b) Asked probablity is P(A|B\')=P(AnB\')/P(B\')=(P(A)-P(AnB))/(1-P(B))=(0.4-0.12)/(1-0.3)=0.4