A seed packaging company purchases 40% of their beans seeds from supplier A and 60% from supplier B and mixes these seeds together. If the bean seed comes from supplier A, the probability it will germinate is 85%. If the bean seed comes from supplier B, the probability it will germinate is 75%.(a) Find the probability P(G) that a seed selected atrandom from the mixed seeds will germinate.
(b) Given that a seed germinates, find the probability that theseed was purchased from supplier A.

A) 0.79

B) 0.43

Explanation:

a. P (G) = Seed germinates either from supplier A or supplier B

P (A chosen) & P (A Seed germinates) or P (B chosen) & P (B seed germinates)

= (0.40 X 0.85) + (0.60 X 0.75) = 0.34 + 0.45

= 0.79

b. P (A/G) = P (G/A) P (A)

                      P (G)

= (0.85 X 0.40) / 0.79 = 0.34 /0.79

= 0.43

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