SOLUTION: A carton contains 15 transistors of which 5 are defective. If a random sample of 6 transistors are drawn from the carton (without replacement) determine the probability of 2 defect

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Question 1149524: A carton contains 15 transistors of which 5 are defective. If a random sample of 6 transistors are drawn from the carton (without replacement) determine the probability of 2 defective valves in the sample.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


solution deleted -- did not read the problem correctly

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
A carton contains 15 transistors of which 5 are defective. If a random sample of 6 transistors are drawn from the carton
(without replacement). Determine the probability of 2 defective highlight%28cross%28valves%29%29 transistors in the sample.
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The sample space in this case is the set of all groups of 6 transistors that can be selected from 15 transistors.


The number of such groups is the number of combinations of 15 items taken 6 at a time

    C%5B15%5D%5E6 = %2815%2A14%2A13%2A12%2A11%2A10%29%2F%281%2A2%2A3%2A4%2A5%2A6%29 = 5005.



The favorable set is the set of all groups of 6 transistors that contain 2 defective and 4 valid transistors.


The number of such groups is


    C%5B5%5D%5E2.C%5B15-5%5D%5E4 = C%5B5%5D%5E2.C%5B10%5D%5E4 = 10*210 = 2100.


The probability under the problem's question is


    P = 2100%2F5005 = 0.4196 = 41.96%  (approximately).    ANSWER

Solved.