# Video: CBSE Class X • Pack 1 • 2018 • Question 7

CBSE Class X • Pack 1 • 2018 • Question 7

03:02

### Video Transcript

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 doubles occur.

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 is one-sixth.

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.