Nico\'s Nuts buys a blend of peanuts and cashews from 2 vendors, with 61% coming

Question

Nico's Nuts buys a blend of peanuts and cashews from 2 vendors, with 61% coming from Brasstown farms and the rest from Rabun farms. The blend from Brasstown is 71% peanuts and 29% cashews, and the blend from Rabun is 51% peanuts and 49% cashews. All nuts are mixed by Nico's before packaging. A random nut is chosen from the mixture a) Find the probability that the nut came from Brasstown, given that it is a peanut. b) Find the probability that the nut came from Rabun, given that it is a cashew. a) The probability that the nut came from Brasstown, given that it is a peanut, is L1 (Do not round until the final answer. Then round to four decimal places as needed.) b) The probability that the nut came from Rabun, given that it is a cashew, is Do not round until the final answer. Then round to four decimal places as needed.)

Explanation / Answer

P(Brasstown farms) = 0.61

P(Rabun farms) = 1 - 0.61 = 0.39

P(peanut/Brasstown farms) = 0.71

P(cashew/Brasstown farms) = 0.29

P(peanut/Rabun farms) = 0.51

P(cashew/Rabun farms) = 0.49

P(peanut) = P(Brasstown farms)*P(peanut/Brasstown farms) + P(Rabun farms)*P(peanut/Rabun farms)

= 0.61*0.71 + 0.39*0.51 = 0.632

P(cashew) = 1 - 0.632 = 0.368

a)

probability that the nut come from Brasstown, given that is a peanut i.e P(Brasstown/ peanut)

= P(Brasstown and peanut)/P(peanut)

= P(Brasstown farms)*P(peanut/Brasstown farms)/P(peanut)

= 0.61*0.71/0.632 = 0.6853

b)

probability that the nut come from Rabun, given that is a cashew i.e P(Rabun/ cashew)

= P(Rabun and cashew)/P(cashew)

= P(Rabun farms)*P(cashew/Rabun farms)/P(cashew)

= P(Rabun farms)*(1- P(peanut/Rabun farms))/P(cashew)

= 0.39*(1-0.51)/0.368 = 0.5193

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