SOLUTION: ABC Ltd . produces cartridges for the latest printer , and they are sold in
boxes of 8. Unfortunately, 2% of them are faulty. Find the probability that a
given box has at least o
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-> SOLUTION: ABC Ltd . produces cartridges for the latest printer , and they are sold in
boxes of 8. Unfortunately, 2% of them are faulty. Find the probability that a
given box has at least o
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Question 1120617: ABC Ltd . produces cartridges for the latest printer , and they are sold in
boxes of 8. Unfortunately, 2% of them are faulty. Find the probability that a
given box has at least one faulty cartridge in it. Answer by Theo(13342) (Show Source):
p is the probability of failure
q is the probability of no failure
x is the number of failures.
n-x is the number of no failures
c(n,x) is the number of ways to get sets of x elements out of sets of n elements without worrying about order within each set.
total probability is always equal to 1.
probability of at least 1 failure is equal to 1 minus probability of no failures.
in your problem.
n = 8
p = .02
q = .98
x = 0 through 8.
p(0) = .02^0 * .98^(8-0) * c(8,0)
this becomes p(0) = 1 * .98^8 * c(8,0) which becomes:
p(0) = 1 * .850763023 * 1 which becomes:
p(0) = 850763023.
probability of at least 1 failure is therefore equal to 1 minus .850763023.
this results in probability of at least 1 failure = .149236977.
all the probabilities of failure are captured in the following excel spreadsheet.
