Answer:
P(X = 0) = 0.0176
P(X = 1) = 0.2348
P(X = 2) = 0.7476
Step-by-step explanation:
Because there are 2 mechanical components you have 3 differents scenarios:
1. The 2 components dont meet the specification (X = 0)
2. 1 of the 2 component doesnt meet the specification (X = 1)
3. The 2 components meet the specification. (X = 2)
P(A) = 0.89
The probability that A doesnt meet the specification is 1- P(A) = 0.11
P(B) = 0.84
The probability that A doesnt meet the specification is 1- P(B) = 0.16
Then using those probabilities to determine the probabilities of each scenario you get:
1. The 2 components dont meet the specification
P (X = 0) = (1 - P(A)) * (1- P(B))
P (X = 0) = 0.11 * 0.16 = 0.0176
2. 1 of the 2 component doesnt meet the specification (X = 1)
P (X = 1) = P(A)*(1- P(B)) + P(B)*(1 - P(A)) /// (The probability that A meets specification and B doesnt or B that meets specification and A doesnt)
P (X = 1) = 0.89*0.16 + 0.84*0.11 = 0.2348
3. The 2 components meet the specification. (X = 2)
P(X = 2) = 0.89*0.84 = 0.7476
