Please answer the second experiment (iv) to (vii) We have a bag that contains 2 red balls, 3 blue balls and 4 green balls. For our firstexperiment, we take a random ball from the bag, observing its colour, return the ball tothe bag, and then take a second ball at random, observing its colour.i) Describe the sample space and event space for this experiment. You do not needto explicitly list every element of the event space.ii) Let BG denote the event in which the first ball drawn is blue, and the second isgreen. Calculate P(BG).iii) Let R denote the event in which either the first or second ball drawn is red,including the case where both are red. Calculate P(R).In a second experiment, we keep the same bag, but instead of returning the first ball tothe bag, we do not replace it before drawing the second.iv) Explain how the probability space for this new experiment differs to that for thefirst experiment.v) Let R1,B1,G be the events in which, respectively, a red, blue or green ball isdrawn first, and G, the event in which a green ball is drawn second. CalculateP(G2|R1), P(G2|B1) and P(G2|G).vi) Using your answer from the previous question, calculate P(G2).vii) Using Bayes' Theorem, calculate P(B||G2).

Answered: Image /qna-images/answer/aeeb52e6-7e9d-499d-ac19-5fabe4fcdb18.jpg

In a second experiment, we keep the same bag, but instead of returning the first ball to the bag, we do not replace it before drawing the second. iv) Explain how the probability space for this new experiment differs to that for the first experiment. v) Let R1,B1,G be the events in which, respectively, a red, blue or green ball is drawn first, and G, the event in which a green ball is drawn second. Calculate P(G2|R1), P(G2|B¡) and P(G2|G). vi) Using your answer from the previous question, calculate P(G2). vii) Using Bayes' Theorem, calculate P(B1|G2).

In a second experiment, we keep the same bag, but instead of returning the first ball to the bag, we do not replace it before drawing the second. iv) Explain how the probability space for this new experiment differs to that for the first experiment. v) Let R1,B1,G be the events in which, respectively, a red, blue or green ball is drawn first, and G, the event in which a green ball is drawn second. Calculate P(G2|R1), P(G2|B¡) and P(G2|G). vi) Using your answer from the previous question, calculate P(G2). vii) Using Bayes' Theorem, calculate P(B1|G2).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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