Friday, 5 September 2014

probability - Expected number of rolls to get all 6 numbers of a die





I've been thinking about this for a while but don't know how to go about obtaining the answer. Find the expectation of the times of rolls if u want to get all 6 numbers when rolling a 6 sided die.



Thanks


Answer



Intuitively



You first roll a die. You get some value. Now, the probability of getting a different value on the next one is 56 . Hence the expected value for different values in two rolls is 65. You continue this and get



66+65+64+63+62+61=14.7 rolls


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