A company manufactures marbles. Over a year, it is observed that 70% of the marbles manufactured pass the quality check and 30% are rejected. 60% of the rejected marbles undergo reprocessing, while the rest go into scrap. What is the probability that out of 15 marbles selected at random exactly 3 marbles go into scrap?
Accepted Solution
A:
The probability that 1 given marble goes into scrap is: (30% chance of rejection)*(40% change of scrap if rejected) = 0.3*0.4 = 0.12. Therefore the probability that a marble does not go into scrap is 1 - 0.12 = 0.88.
Based on a binomial distribution: P = (15C3)(0.12)^3 (0.88)^(15-3) = 0.1696.