On any given day, a certain machine has either no malfunctions or exactly one ma
ID: 3041645 • Letter: O
Question
On any given day, a certain machine has either no malfunctions or exactly one malfunction. The probability of malfunction on any given day is 0.40. Machine malfunctions on different days are mutually independent. a. Calculate the probability that the machine has its first malfunction on the fifth day, given that the machine has not had malfunctions in the first three days Calculate the probability that the machine has its third malfunction on the fifth day, given that the machine has not had three malfunctions in the first three days. b.Explanation / Answer
Define Success = 1 as Machine has Malfunctioning. It is given that p=P[Success] = 0.40
Define Failure = 0 as Machine has No Malfunctioning. q=1-p=P[Failure] = 0.60
Define:
X1 as functioning status of Machine on 1st Day
X2 as functioning status of Machine on 2nd Day
.
.
.
Xn as functioning status of Machine on nth Day
Each random variable has Bernoulli distribution with p=0.40
= P[X5 = 1|X1=0, X2=0, X3=0] = P[X5 = 1, X1=0, X2=0, X3=0] / P[X1=0, X2=0, X3=0] = P[X5 = 1] = 0.4
P[Impossible Event]=0
The underlying event is impossible because it is not possible to occur third Malfunction on Fifth day and NO malfunction on first Three days. Because every day Machine status is 0 or 1.
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