Question

At a quality control checkpoint on a manafacturing assembly line, 10% of the items failed check A, 12% failed check B, and 3% 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?

Answer 1

a. 10% out of 100% failed A or 10/100
3% of 100% failed A & B or 3/100
3% that failed A(10%) also failed B or 3/10

b. 12% out of 100% failed B
3% out of 100% failed A & B or 3/12

c. failed A - 10%
failed B - 12%
sub total 22%(-3% counted double-failed both)
= 19% total

d. 100%-19% that failed =81% chance product did not fail.