UNH About Probability Questions

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WNFBA99

Mathematics

University of New Hampshire

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There are two quick questions, which won't take your much time. I need the experimental tutor who good at probability. Just paying attention on reading question carefully and answers them as detailedly as you can.

For these short questions, the advantage is that you have plenty of time to complete it. Looking forward to working with you. Thank you for your attention.

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PROBLEM 5. You have a box containing 6 balls, 2 of which are blue and 4 of which are red. You play the following game: repeatedly, you draw a ball from the box, look at its color, and place it back in the box. Each draw is independent of the other ones and in each draw you are equally likely to select any of the balls. The game ends the moment you draw a blue ball for the second time. What is the probability that the game ends on the fourth draw? PROBLEM 6. Alice and Bob each own a coin. Alice's coin comes up heads with probability pa. Bob's coin comes up heads with probability PB. They play the following game against each other. At each round, they both toss their own coin. If for that round both coins come up heads or both coins come up tails, then the game continues. If one of the coins comes up heads and the other comes up tails, the person whose coin came up heads wins and the game ends. (a) In a given round, what is the probability that Alice wins that round? (b) What is the probability that the game ends after two rounds, with Alice winning? (c) What is the probability that the game ends after k rounds, with Alice winning? Your answers should be in terms of Pa, PB, (and k for part (c)). All coin tosses are independent of each other.
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