SOLUTION: Before a DVD leaves the factory, it is given a quality control check. The probabilities that a DVD contains 0, 1, or 2 defects are 0.90, 0.06, and 0.04, respectively. In a sample

Algebra ->  Probability-and-statistics -> SOLUTION: Before a DVD leaves the factory, it is given a quality control check. The probabilities that a DVD contains 0, 1, or 2 defects are 0.90, 0.06, and 0.04, respectively. In a sample       Log On


   

Question 1192618: Before a DVD leaves the factory, it is given a quality control check. The probabilities that a DVD contains 0, 1, or 2 defects are 0.90, 0.06, and 0.04, respectively. In a sample of 12 recorders, find the probability that 8 have 0 defects, 3 have 1 defect, and 1 has 2 defects.
Answer by ikleyn(52832) About Me  (Show Source):
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Before a DVD leaves the factory, it is given a quality control check.
The probabilities that a DVD contains 0, 1, or 2 defects are 0.90, 0.06, and 0.04, respectively.
In a sample of 12 recorders, find the probability that 8 have 0 defects, 3 have 1 defect, and 1 has 2 defects.
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Use the trinomial distribution formula


    P = %2812%21%2F%288%21%2A3%21%2A1%21%29%29%2A0.9%5E8%2A0.06%5E3%2A0.04%5E1 = %28%2812%2A11%2A10%2A9%29%2F6%29%2A0.9%5E8%2A0.06%5E3%2A0.04 = 0.007364.    ANSWER

Solved.

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On trinomial distribution, see and learn from your textbook or from these Internet sources

https://online.stat.psu.edu/stat414/lesson/17/17.3

https://en.wikipedia.org/wiki/Multinomial_distribution