probability question… need help…?
Thursday, July 22nd, 2010 at
4:24 pm
Question by Juan C: probability question… need help…?
A printing company’s bookbinding machine has a probability of 0.005 of producing a defective book. If this machine is used to bind three books…
how do you find the probability that…
a.) none of the books are defective
b.) at least one of the book is defective
c.) all of the books are defective
Best answer:
Answer by fcas80
a. .995*.995*.995
b. 1 – .995*.995*.995
c. .005*.005*.005
Add your own answer in the comments!
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Filed under: binding machine review
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Assuming independent outcomes:
a.) (1-.005)^3 = 0.985074875
b.) 1 minus the answer to (a) = 0.014925125
c.) 0.005^3 = 0.000000125
However, if the outcomes are NOT independent, then all bets are off. E.g., if the bookbinding machine has a tendency to produce defects in clusters, then (a) is higher, (b) is lower, and (c) is higher.
Binomial probability
nCr p^r q^ (1-r)
where n = total number of books
r = number of successes
p = prob of success
C = combinations.
none is 3C0 (0.005)^0 (0.995)^3 ? 0.985
at least 1 is all but none so 1 – 0.985 = 0.015
and for all 3, use the formula like in a)