Answer:
a) For this case we have 4 programs so then if we define the event R that a CD is tested we have the following probability for each test:
The failure probability for each program are given by:
For this case we assume that each test is independet form the others.
We can calculate the probability that all 4 programs works properly like this:
So then the probability that any program fails would be given by:
And if we use the fact that we have 4 possible test the true probability of interest would be:
b)
And replacing we got:
c) From part a we now that the probability that any program fails would be given by:
So then if we have 100 CDs the expected number of rejected Cd's are:
Step-by-step explanation:
Part a
For this case we have 4 programs so then if we define the event R that a CD is tested we have the following probability for each test:
The failure probability for each program are given by:
For this case we assume that each test is independet form the others.
We can calculate the probability that all 4 programs works properly like this:
So then the probability that any program fails would be given by:
And if we use the fact that we have 4 possible test the true probability of interest would be:
Part b
For this case we want the probability that it failed program 2 or 3
So then we can find this probability like this:
And replacing we got:
Part c
From part a we now that the probability that any program fails would be given by:
So then if we have 100 CDs the expected number of rejected Cd's are: