If two dice are rolled, what is the probability that the sum of the numbers on the dice is 7?
Practice Questions
1 question
Q1
If two dice are rolled, what is the probability that the sum of the numbers on the dice is 7?
1/6
1/12
1/36
5/36
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.
Questions & Step-by-step Solutions
1 item
Q
Q: If two dice are rolled, what is the probability that the sum of the numbers on the dice is 7?
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.
Steps: 6
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.
