Answer:
(a) P(B) = 0.008, (b) P(A∩B) = 0, (c) Yes, A and B are mutually exclusive events, (d) P(A∪B)=0.948, (e) 0.948, (f) 0.06
Step-by-step explanation:
We have three different posibilities
A: fill to specification
B: underfill
C: overfill
in probability the sum of the different events which are mutually exclusive should sum to 1, so, we should have
(a) P(B) = 1 - P(A)-P(C) = 1-0.940-0.052=0.008
(b) P(A∩B)=probability that the machine fill to specification and underfill = 0 because a machine can't fill to specification and underfill at the same time
(c) Yes, A and B are mutually exclusive events, because a machine can't fill to specification and underfill at the same time
(d) Because A and B are mutually exclusive events we should have that
P(A∪B)=P(A)+P(B)=0.940+0.008=0.948
(e) The probability that the machine does not overfill is the same that the probability that the machine fill to specification plus the probability that the machine underfill, i.e, the probability that the machine does not overfill is P(A)+P(B)=0.948, because does not overfill is equivalent either to fill to specification or to underfill.
(f) The probability that the machine either overfill or underfills is
P(C∪B)=P(C)+P(B)=0.052+0.008=0.06 because C and B are mutually exclusive events.
