Using the data above find the probability that an email is spam or not if it has

Question

Using the data above find the probability that an email is spam or not if it has. groceries. "Money" and "unsubscribe" and not containing "Viagra" "Viagra" and "groceries", but not "money" or "unsubscribe" A retail store carries a product that is supplied by three manufactures. A. B. and C. and 30% from A. 20% from B and 50% from C. It is known that 2% of the products from A are defective. 3% from B ate defective, and 5% from C are defective. If a product is randomly selected from this store, what is the probability that it is defective? If a defective product is found what is the probability that it was from U'

Explanation / Answer

3 products are A, B, and C.
C produces 50% of the output.
A produces 30% of the output.
B produces 20%of the output.

P(A) = 30/100; and P(D|A) = 2/100

p(B) = 20/100 and P(D|B) = 3/100

P(C) = 50/100 and P(D|C) = 5/100

(A) P(D) = 1/25 * 3/10 + 3/100 * 1/50 + 1/2 * 1/20 = 0.0376 = 3%

(B) P(B|D) = ((20 * 3)/100)/3 = 0.6/3 = 6/30 = 20/100 = 20%

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