If I roll two dice 4 times, what is the probability of getting doubles at least once?

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Answer 1 · 2017-11-04T07:01:18

#671/1296#

If you roll two dice, there are #6xx6 = 36# different combinations of numbers. Of these, there will be #6# doubles

So, the probability of rolling a double is #P("double") =6/36 =1/6#
The probability of not rolling a double is #5/6#

In 4 throws, 'At least one double' means there can be one, two, three, or four doubles.

#P("at least one double") = 1-P("no double")#

#P("no doubles, 4 times in a row") = 5/6xx5/6xx5/6xx5/6 = (5/6)^4#

#P("at least one double") = 1-(5/6)^4 = 671/1296#

This is clearer if you draw a branch diagram. For each of the four throws, there are only two outcomes we need to consider:

Either a double is thrown #(P= 1/6)# or not thrown #(P=5/6)#