6. Suppose you roll a fair six-sided die repeatedly until the first time you roll a number that you have rolled before. a) For each r = 1, 2, ... calculate the probability på that you roll exactly r times. b) Without calculation, write down the value of p1 + P2 + + P10. Explain. c) Check that your calculated values of på have this value for their sum.

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6. Suppose you roll a fair six-sided die repeatedly until the first time you roll a number
that you have rolled before.
a) For each r = 1, 2, ... calculate the probability p, that you roll exactly r times.
b) Without calculation, write down the value of p₁ + p2 +
+ P10. Explain.
c) Check that your calculated values of p, have this value for their sum.
Transcribed Image Text:6. Suppose you roll a fair six-sided die repeatedly until the first time you roll a number that you have rolled before. a) For each r = 1, 2, ... calculate the probability p, that you roll exactly r times. b) Without calculation, write down the value of p₁ + p2 + + P10. Explain. c) Check that your calculated values of p, have this value for their sum.
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