An urn has one blue ball and one red ball. Andy draws a ball from the...

 

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An urn has one blue ball and one red ball. Andy draws a ball from the urn randomly, observes the color of the drawn ball, and puts the ball back in the urn. He repeats until he sees the blue ball twice or he has made 4 draws. For each draw, the probability of getting the blue ball is 1/3 and the probability of getting the red ball is 2/3, independent to other draws. (a) Draw the tree diagram and show the probabilities of all leaves. (b) What is the probability that Andy sees the blue ball more times than he sees the red ball? (c) What is the probability that Andy sees the blue ball more times than he sees the red ball given that his second draw is a blue ball? An urn has one blue ball and one red ball. Andy draws a ball from the urn randomly, observes the color of the drawn ball, and puts the ball back in the urn. He repeats until he sees the blue ball twice or he has made 4 draws. For each draw, the probability of getting the blue ball is 1/3 and the probability of getting the red ball is 2/3, independent to other draws. (a) Draw the tree diagram and show the probabilities of all leaves. (b) What is the probability that Andy sees the blue ball more times than he sees the red ball? (c) What is the probability that Andy sees the blue ball more times than he sees the red ball given that his second draw is a blue ball?