Question

Two production lines produce the same part. Line 1 produces 1,000 parts per week of which 100 are defective. Line 2 produces 2,000 parts per week of which 150 are defective. If you choose a part randomly from the stock what is the probability it is defective? If it is defective what is the probability it was produced by line 1?

Answer 1

Answer:

Two production lines produce the same parts per week of which 100 are defective. Line 2 produces 2,000 parts per week of which 150 are defective. If you choose a part randomly from the stock what is the probability it is defective? If it is defective what is the probability it part. Line 1produces 1,000 produced by line 1?

Answer

Answer:(a) 0.0833 or 8.33%(b) 0.40 or 40%Step-by-step explanation:Parts line one (n1) = 1,000 partsDefects line one (d1) = 100 partsParts line two (n2) = 2,000 partsDefects line two (d2) = 150 partsTotal number of parts (n) = 3,000 partsa. Probability of a randomly selected part being defective:$P(d) = \frac{d_1+d_2}{n_1+n_2}=\frac{100+150}{1,000+2,000}\P(d) =0.0833=8.33\%$The probability is 0.0833 or 8.33%b. Probability of a part being produced by line one, given that it is defective:$P(1|d)=\frac{P(1\cap d)}{P(1\cap d)+P(2\cap d)}\P(1|d)=\frac{\frac{100}{3,000} }{\frac{100}{3,000}+\frac{150}{3,000}}\P(1|d)=0.4 = 40\%$The probability is 0.40 or 40%.

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