Question

Ninety-five percent of the sneakers manufactured by a shoe company have no defects. In order to find the 5% that do have defects, inspectors carefully look over every pair of sneakers. Still the inspectors sometimes make mistakes because 4% of the defective pairs pass inspection and 2% of the good pairs fail to pass the inspection test. IF a par of sneakers does NOT pass inspection, what is the probability that id does NOT have a defect?

Answer 1

5% of shoes have a defect,
96% of these do not pass inspection.
95% of shoes do not have a defect,
2% of these do not pass inspection.

Calculate % of shoes that do not pass inspection:
If you have 10000 pairs, the defective 5% is represented by 500 pairs.
96% of these do not pass inspection, which is 4.75% of the total.

The acceptable 95% is represented by 9500 pairs.
2% of these do not pass inspection, which is 1.9% of the total.

6.65% of all shoes do not pass inspection.
out of 665 failing shoes, 190 are not defective.

If a pair of shoes does not pass inspection, the probability that they are not defective is 38:133