Please explain your reasoning to solve this problem. Provide as much details as

Question

Please explain your reasoning to solve this problem. Provide as much details as possible. Thank you =)!

Problem A manufactwe bugs comonents in eual amdunts from thre dfferent supplies. The prbablty at compoments fRom Suglier A are bod is 0.1, that components rom sugplier B are bad is 0.15, and hat oomponent from sugolier C are bad 0.05 (a) The probability ata comgonent selected at randam wil be bad )a cogonen dt bebadh what is the grobability that componen+ selec at ran0m will be bad, what is he probabi a COmponent1 it came from supplier b?

Explanation / Answer

Since the Supplier is buying component in equal amounts,

P(A) = P(B) = P(C) = 1/3

Also it is given that:

P(Bad | A) = 0.10

P(Bad | B) = 0.15

P(Bad | C) = 0.05

a) P(Bad) = P(A)*P(Bad | A) + P(B)*P(Bad | B) + P(C)*P(Bad | C)

P(Bad) = (1/3)*0.1 + (1/3)* 0.15 + (1/3)*0.05

P(Bad) = 1/10

P(Bad) = 0.10

b) P(B | Bad) = P(B and bad) / P(Bad) = P(Bad | B)*P(B) / P(Bad) = (0.15*1/3) / 0.10 = 0.15/0.30 = 0.50

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