Answer to Question #151136 in Statistics and Probability for Anirrban

Question

A produce shipper has 10,000 boxes of bananas from Ecuador and Honduras. An inspection has determined the following information

# of boxes Damaged fruit Overripe fruit

Ecuadoran 6,000 200 840
Honduran 4,000 365 295

(a)What is the probability that a box selected at random will contain damaged fruit? Overripe fruit?
(b)What is the probability that a randomly selected box is from Ecuador
Or Honduras?
(c)Given that a randomly selected box contains overripe fruit, what is the probability that it came from Honduras?
(d)If damaged fruit and overripe fruit are mutually exclusive, what is the probability that a box

Answer 1

(a)What is the probability that a box selected at random will contain damaged fruit? Overripe fruit?

P(damaged fruit) = (200+365)/10000 = 0.0565

P(overtipe fruit) = (840+295)/10000 = 0.1135

(b)What is the probability that a randomly selected box is from Ecuador

Or Honduras?

P(from Ecuador) = 6000/10000 = 0.6

P(from Honduras) = 4000/10000 = 0.4

(c)Given that a randomly selected box contains overripe fruit, what is the probability that it came from Honduras?

P(from Honduras | overripe fruit) = 295/(840+295) = 295/1135 = 0.260

(d)If damaged fruit and overripe fruit are mutually exclusive, what is the probability that a box

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