Two dice are rolled together. Find the probability that the
numbers they land on 1) are the same and 2) sum to 10.
The probability of any event is the
number of ways that an event can occur over all possible outcomes. Our first event is the probability
that the numbers rolled are the same. You might call it the probability
of getting doubles. We need to know how many ways can
We have two dice. One probability is that they both
rolled one or two. We could get threes, fours, fives,
or sixes. There are six ways doubles can
occur. And that means our numerator here
is a six. And now, we need all outcomes. All possible outcomes from the
first die are the numbers one through six. So we have a six outcomes. For the second die, there would
again be six possible outcomes. We multiply these two possible
outcomes together to get 36. There are 36 different possible
outcomes and that is our denominator.
Six over 36 can be simplified. Both the numerator and the
denominator are divisible by six. Six divided by six is one. 36 divided by six equals six. The probability of getting doubles
We follow the same procedure for
the second option: finding the probability that the dice roll sums to 10. To find this probability, we need
to first think about the number of ways that a dice roll can end up with a sum of
10. We know our first die has numbers
one through six, so does our second. Five plus five equals 10, four plus
six equals 10, and six plus four equals 10.
The pairings that sum to 10 are
four, six; five, five; and six, four. There are three ways our event can
occur. The denominator here is the same
denominator as the first part. There are 36 possible outcomes when
you roll two dice.
The probability that our roll sums
to 10 equals three over 36. But again, this can be
simplified. Both the numerator and the
denominator are divisible by three. Three divided by three equals
one. 36 divided by three equals 12. The probability that the roll sums
to 10 is one twelfths.