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At a quality control checkpoint on a manufacturing assembly line, 8% of the items failed check A, 10% failed check B, and 2% failed both checks A and B.

a. If a product failed check A, what is the probability that it also failed check B? b. If a product failed check B, what is the probability that it also failed check A?
c. What is the probability that a product failed either check A or check B?
d. What is the probability that a product failed neither check A nor check B?


I am not good with probability and the percentages are really throwing me off. Any help would be great.

  • Math -

    a)1/4 (25%) of those that failed A also failed B. That leaves you with 1/4 or 8% or 2% failing both.
    b) Similarly, 1/5 (20%) of those that failed B also failed A.
    c) Add the fractions that failed A only, B only, and both. I get 8% + 6% + 2% = 16%
    That fraction failed A only, B only or both.
    d) 84%

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