If two 6-sided number cubes are rolled, what is the probability that 6-2 will be rolled?

Question

anonymous · Answer

2 out of 12

perl · Answer

I am not sure what you mean by rolling 6-2. 
Is the question what is the probability of rolling a 4?

anonymous · Answer

Assuming a fair die the probability of not rolling a six is 5/6.

The probability of not rolling a six on the second roll is also 5/6.

As these two events are independent the probability of both occurring, that is no six on either roll, is the two probabilities multiplied together

     5/6×5/6=25/36

The probability of getting at least one six is the complement of the probability of getting no sixes

     1−25/36=11/36≈30.6

You can extend this analysis to three or more rolls of the die. For three rolls

     1−5363=216−125216=91/216≈42.1

which is still less than half. For four rolls we have

     1−5464=1296−6251296=671/1296≈51.8

which is finally (just) over half a chance of getting at least one six.

Did you know that you are about as likely to not roll a six ten times in a row, as you are to roll a six on the first roll. That is:

     1−510610≈83.8

No wonder getting that double to get out of jail in Monopoly sometimes seems to take forever!