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?

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.

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aramisdegaula1977 aramisdegaula1977 · Answer 2 · 2019-09-13T03:30:54+02:00

Answer:

Probability that exactly 3 marbles are sent to scrap is 0.1696

Step-by-step explanation:

The percentage of marbles of the initial production that is rejected is 30%. On the other hand, of that 30% 40% is sent to scrap metal. Where the percentage of marbles sent to scrap is (30%) (40%) = 12%. In the same way, the probability that any marble will be sent to scrap is 0.12.

Now, the number of marbles that should be sent to scrap, within a group of 15 marbles, is a binomial random variable with parameters n = 15 and p = 0.12. Therefore, the probability that exactly 3 marbles are sent to scrap is:

[tex]P(X = 3) = _{n}C_{x} (p)^x(1-p)^{n-x} = _{15}C_{3} (0.12)^3(0.88)^{12} = 0.1696[/tex]