suppose box a contains 4 red and 5 blue chips and box b contains 6 red and 3 blue chips. a chip is chosen at random from box a and placed in box b. then a chip is chosen at random from among those now in box b. what is the probability a blue chip was transferred from box a to box b, given that the chip chosen from box b is red?

Question

20-12-2022
Mathematics

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suppose box a contains 4 red and 5 blue chips and box b contains 6 red and 3 blue chips. a chip is chosen at random from box a and placed in box b. then a chip is chosen at random from among those now in box b. what is the probability a blue chip was transferred from box a to box b, given that the chip chosen from box b is red?

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debjitbhowal4568 debjitbhowal4568 · Answer 1 · 2022-12-25T14:08:52-05:00

The probability that a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red is 0.517.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Let A be the event in which coin chosen from box B is red.

Let B be the event in which blue poker chip transferred.

Probability of choosing a red coin:

a) when a red coin is chosen from box A = [tex]\frac{7}{10}[/tex] × [tex]\frac{4}{9}[/tex]

b) when a blue coin is chosen from box A = [tex]\frac{6}{10}[/tex] × [tex]\frac{5}{9}[/tex]

∴ P(A) = [tex]\frac{7}{10}[/tex] × [tex]\frac{4}{9}[/tex] + [tex]\frac{6}{10}[/tex] × [tex]\frac{5}{9}[/tex] = 0.6444

When blue chip is transferred and red coin chosen:

Probability = [tex]\frac{6}{10}[/tex] × [tex]\frac{5}{9}[/tex]

∴ P(A∩B) = [tex]\frac{6}{10}[/tex] × [tex]\frac{5}{9}[/tex] = 0.33

Now, the probability that a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red is:

P(B|A) = P(A∩B)/P(A) = 0.33/0.644 = 0.517

Thus, the probability that a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red is 0.517.

To learn more about probability, visit brainly.com/question/30034780

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