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標題:
發問:
Suppose I roll a fair six-sided die repeatedly until the first time I roll a number that I have rolled before. For each r=1,2...calculate the probability pr that you roll exactly r times.
最佳解答:
At most 7 times. p1 = 6/6 * 0 = 0 p2 = 6/6 * 1/6 = 1/6 p3 = 6/6 * 5/6 * 2/6 = 5/18 p4 = 6/6 * 5/6 * 4/6 * 3/6 = 5/18 p5 = 6/6 * 5/6 * 4/6 * 3/6 * 4/6 = 5/27 p6 = 6/6 * 5/6 * 4/6 * 3/6 * 2/6 * 5/6 = 25/324 p7 = 6/6 * 5/6 * 4/6 * 3/6 * 2/6 * 1/6 * 6/6 = 5/324 Verify : p1 + p2 + p3 + p4 + p5 + p6 + p7 = 0 + 1/6 + 5/18 + 5/18 + 5/27 + 25/324 + 5/324 = 1
其他解答:D1B39E80075704FD
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Roll a die ----quick!!!發問:
Suppose I roll a fair six-sided die repeatedly until the first time I roll a number that I have rolled before. For each r=1,2...calculate the probability pr that you roll exactly r times.
最佳解答:
At most 7 times. p1 = 6/6 * 0 = 0 p2 = 6/6 * 1/6 = 1/6 p3 = 6/6 * 5/6 * 2/6 = 5/18 p4 = 6/6 * 5/6 * 4/6 * 3/6 = 5/18 p5 = 6/6 * 5/6 * 4/6 * 3/6 * 4/6 = 5/27 p6 = 6/6 * 5/6 * 4/6 * 3/6 * 2/6 * 5/6 = 25/324 p7 = 6/6 * 5/6 * 4/6 * 3/6 * 2/6 * 1/6 * 6/6 = 5/324 Verify : p1 + p2 + p3 + p4 + p5 + p6 + p7 = 0 + 1/6 + 5/18 + 5/18 + 5/27 + 25/324 + 5/324 = 1
其他解答:D1B39E80075704FD
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