SOLUTION: please help me answer this question: A factory makes resistors using two machines (A and B). 36% are made by machine A and the rest by B. 5% of components made by machine A are

Algebra ->  Probability-and-statistics -> SOLUTION: please help me answer this question: A factory makes resistors using two machines (A and B). 36% are made by machine A and the rest by B. 5% of components made by machine A are       Log On


   

Question 1115445: please help me answer this question:
A factory makes resistors using two machines (A and B). 36% are made by machine A and the rest by B. 5% of components made by machine A are defective, while 2% of those made by B are defective. Given that a resistor chosen at random is defective, what is the probability that it was made by machine A?
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
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Of every 10000 resistors, 36%, i.e. %2810000%2F100%29%2A36 = 3600 are made by the machine A, and every 5% of these 3600, i.e. %283600%2F100%29%2A5 = 180 are defective.


Of every 10000 resistors, the rest 64%, i.e. %2810000%2F100%29%2A64 = 6400 are made by the machine B, and every 2% of these 6400, i.e. %286400%2F100%29%2A2 = 128 are defective.


Given that a resistor chosen at random is defective means that you choose it from 180+128 = 308 defective.


It is your space of events under the given restriction.


Then the conditional probability under the question is  180%2F308 = 0.584 = 58.4%.

Solved.