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A die is rolled repeatedly until two consecutive rolls have the same number. How many times do
you expect to roll the die?
Solution
Let E be the expected number of rolls.
Suppose, we expect the number 6 to come twice. Assume that there are 6 rolls until a 6 comes.
Now, there is a 1/6 chance to roll once more and 5/6 chance of starting all over again.
Thus, E=6+1/6*1+5/6(E+1)
E=42

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