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If two dice are rolled, what is the probability that the sum of the numbers on t

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Question: If two dice are rolled, what is the probability that the sum of the numbers on the dice is 7?

Options:

  1. 1/6
  2. 1/12
  3. 1/36
  4. 5/36

Correct Answer: 1/6

Solution: 

The combinations that give a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), totaling 6 combinations. The total outcomes are 36, so the probability is 6/36 = 1/6.

If two dice are rolled, what is the probability that the sum of the numbers on t

Practice Questions

Q1
If two dice are rolled, what is the probability that the sum of the numbers on the dice is 7?
  1. 1/6
  2. 1/12
  3. 1/36
  4. 5/36

Questions & Step-by-Step Solutions

If two dice are rolled, what is the probability that the sum of the numbers on the dice is 7?
  • Step 1: Understand that when two dice are rolled, each die has 6 faces with numbers from 1 to 6.
  • Step 2: Calculate the total number of possible outcomes when rolling two dice. Since each die has 6 faces, the total outcomes are 6 (from the first die) multiplied by 6 (from the second die), which equals 36.
  • Step 3: Identify the combinations of numbers on the two dice that add up to 7. These combinations are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).
  • Step 4: Count the number of combinations that give a sum of 7. There are 6 combinations.
  • Step 5: Calculate the probability of rolling a sum of 7 by dividing the number of successful outcomes (6) by the total number of outcomes (36). This gives us 6/36.
  • Step 6: Simplify the fraction 6/36 to get the final probability, which is 1/6.
  • Probability – Understanding how to calculate the likelihood of an event occurring based on favorable outcomes over total outcomes.
  • Combinatorics – Identifying and counting the different combinations that can result in a specific outcome when rolling dice.
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