GCSE Mathematics Question Analysis Topic: Mathematics - Probability
Exam Question:
In a factory which manufactures bolts, machines A, B and C manufacture 30%, 50% and 20% of the bolts respectively. Of their output 3%, 4% and 1% respectively are defective bolts. A bolt is drawn at random from the product and is found to be defective. Find the probability that this is not manufactured by machine B.
Answer:
For GCSE Mathematics, you should know:
Let A, B and C be the bolts manufactured by companies A, B and C respectively, and D be the defective bolts taken.
P(A) = 3 / 10, P(B) = 1/2, P(C) = 1/5
P(D | A) = 3 / 100, P(D | B) = 4 / 100, P(D | C) = 1 / 100
Now, the probability that a defective bolt is drawn from machine B is:
P(B | D) = P(B) x P(D | B) / P(A) x P(D | A) + P(B) x P(D | B) + P(C) x P(D | C)
P(B | D) = 20 / 31
Hence, the probability that the defected bolt is NOT manufactured by machine B is 1 - (20 / 31) = 11 / 31.
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