More hitting 10. Suppose you have a biased coin which comes up heads with probability 7/9...

 

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More hitting 10. Suppose you have a biased coin which comes up heads with probability 7/9 and tails with probability 2/9. Suppose you toss the coin repeatedly, with heads worth 2 and tails worth 3, and add up the score as you go along. Let pn be the probability that you'll hit n. (a) Fill in the entries of the table at the right. (b) Use the trains method to find formula for pn. Check your formula with a direct calculation of p2 and compare with the table. As a special case, provide the probability that you'll hit 10. n 0 1 2 More hitting 10. Suppose you have a biased coin which comes up heads with probability 7/9 and tails with probability 2/9. Suppose you toss the coin repeatedly, with heads worth 2 and tails worth 3, and add up the score as you go along. Let pn be the probability that you'll hit n. (a) Fill in the entries of the table at the right. (b) Use the trains method to find formula for pn. Check your formula with a direct calculation of p2 and compare with the table. As a special case, provide the probability that you'll hit 10. n 0 1 2

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