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Suppose there are two boxes; in box 1 there are 3 times more green balls than red balls, and in box 2 there are 5 red balls and 8 green ones. We choose one of the boxes at random (that is P (B1) = P(B2) = 0.5), and then 3 balls are randomly taken from that box with replacement. Notice that the actual number of colored balls in box 1 is not given, which causes no problem since the drawings are done with replacement. 1. Calculate the following probabilities by theoretical approach and include the calculations and the results in your report: a) The probability that 2 red balls and 1 green ball are drawn (P(2R n 1G) =?) b) If all 3 balls are green what is the probability that box 1 was chosen (P(B1|3G) =?)

Suppose there are two boxes; in box 1 there are 3 times more green balls than red balls, and in box 2 there are 5 red balls and 8 green ones. We choose one of the boxes at random (that is P (B1) = P(B2) = 0.5), and then 3 balls are randomly taken from that box with replacement. Notice that the actual number of colored balls in box 1 is not given, which causes no problem since the drawings are done with replacement. 1. Calculate the following probabilities by theoretical approach and include the calculations and the results in your report: a) The probability that 2 red balls and 1 green ball are drawn (P(2R n 1G) =?) b) If all 3 balls are green what is the probability that box 1 was chosen (P(B1|3G) =?)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Suppose there are two boxes; in box 1 there are 3 times more green balls than red balls, and in box 2 there are 5 red balls and 8 green ones. We choose one of the boxes at random (that is P(B1) = P(B2) = 0.5), and then 3 balls are randomly taken from that box with replacement. Notice that the actual number of colored balls in box 1 is not given, which causes no problem since the drawings are done with replacement. 1. Calculate the following probabilities by theoretical approach and include the calculations and the results in your report: a) The probability that 2 red balls and 1 green ball are drawn (P(2R n 1G) =?) b) If all 3 balls are green what is the probability that box 1 was chosen (P(B1|3G) =?)
Transcribed Image Text:Suppose there are two boxes; in box 1 there are 3 times more green balls than red balls, and in box 2 there are 5 red balls and 8 green ones. We choose one of the boxes at random (that is P(B1) = P(B2) = 0.5), and then 3 balls are randomly taken from that box with replacement. Notice that the actual number of colored balls in box 1 is not given, which causes no problem since the drawings are done with replacement. 1. Calculate the following probabilities by theoretical approach and include the calculations and the results in your report: a) The probability that 2 red balls and 1 green ball are drawn (P(2R n 1G) =?) b) If all 3 balls are green what is the probability that box 1 was chosen (P(B1|3G) =?)
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