Q1. A: A battery is provided by Supplier A
B: A battery is provided by Supplier B
P (A) = 0.55,
P (B) = 0.45
D: A battery is defective
(i)
(ii)
P(D|A) = 0.05
P (D|B) = 0.04
Then, P (D) = Probability that a battery is defective
= P (D|A) * P (A) + P (D|B)* P (B)
= 0.05 * 0.55 + 0.04*0.45
= 0.0455
The desired probability = 1-P(D) = 1-0.0455 = 0.9545
Let us define the event
T: The toy car is OK/ non- defective.
P (T) = P (S1)*P (S2)*P (S3)*P (S4)
Where
Si: Event that stage i of assembling the toy car is accurate, i =1,2,3,4
P(T) = 0.92*0.92*0.92*0.92 = 0.716
Therefore, this strategy will not result in more than 85% of the cars to be perfect.
Q2. E1: Robert is exported to USA
E2: Robert is exported to China
E3: Robert is exported to Spain
R: Robert requires reinstallation of speech software
(i)
Country
USA
China
Spain
P(Ei)
0.35
0.2
0.45
P(R/Ei)
0.05
0.2
0.1
P(R∩Ei)
0.0175
0.04
0.045
P(R) = P(R∩E1) +
P(R∩E2) + P(R∩E3)
= 0.0175 +
0.04 + 0.045
= 0.0125
P(Ei/R)
0.17073
0.39024
0.43902
(ii) Total number of complaints = 300
Country
USA
China
Spain
Expected no. of complaints
300*0.17073 = 51.22
300*0.39024 = 117.07
300*0.43902 = 131.71
Expected repair cost
51.22*2500 = 128048.78
117.07*1200 = 140487.81
131.71*1500 = 197560.976