I've tried using Bayes Theorem and Tree diagram for this problem. I seem to be missing something. Can someone help?
Q:The market is equipped with the same product by three factories. 50% of the market is supplied by the first factory, 30% - by the second factory. The average percentage of deficiencies in the production of the first factory is 3%, of the second is 4% and the third - 5%. The bought element appeared to be defective. Calculate the probability that it comes from the second factory. From which factory is it most likely to buy the product?
Suppose you have 1,000 products. The total number of defectives are 37 so divided:
15 from Factory 1 ; ($1000\times50\%\times 3\%\ $)
12 from Factory 2 ; ($1000\times 30\%\times 4\%\ $)
10 from Factory 3 ; ($1000\times 20\%\times 5\%\ $)
Thus, given a defective (37 choices), the probability that it comes from Factory 1 is simply
$\frac{15}{37}$
from the second Factory $\frac{12}{37}$ and from the third Factory $\frac{10}{37}$