A factory produces fuses, which are packaged in boxes of 16. Three fuses are selected at random from each box for inspection. The box is rejected if at least one of the three fuses is defective. What is the probability that a box containing six defective fuses will be rejected?

Answer 1

p = probability defective = 6/16 = .375
1 - p = 10/16 = .625 = probability good

we do three trials on the box. They all must be good if it is to pass
probability of first trial fuse good = 10/16
probability of second choice being good fuse = 9/15
third = 8/14
so probability of passing = (10*9*8)/(16*15*14) = .0762
so probability of rejection = 1-.0762 = .924

Answer 2

arithmetic!
(10*9*8)/(16*15*14) = .2143
1 - .2143 = .7857

Answer 3

the probability of at least one being defective equals

1 minus the probability that all three are good

1 - (5/8)^3 = .756 (approx)