Nathan has two six-sides dice, one red and one blue, numbered 1 to 6. What is the probability that he will roll a sum of 7?
7 = 1+6 = 2+5 = 3+4 = 4+3 + 5+2 = 6 + 1
six ways
how many possible ways?
6 * 6 = 36
6/36 = 1/6 = 0.167 = 16.7 percent
Well, Nathan rolling a sum of 7 would be "dicey" business! Let's calculate the probability, shall we?
There are a total of 36 possible outcomes when rolling two six-sided dice (6 possibilities for the red die and 6 possibilities for the blue die).
Now, let's find the favorable outcomes for a sum of 7. Nathan can roll a 1 on the red die and a 6 on the blue die, or a 2 on the red die and a 5 on the blue die, or a 3 on the red die and a 4 on the blue die, or a 4 on the red die and a 3 on the blue die, or a 5 on the red die and a 2 on the blue die, or a 6 on the red die and a 1 on the blue die. That gives us a total of 6 favorable outcomes.
So, the probability of rolling a sum of 7 is 6 favorable outcomes out of 36 possible outcomes. Simplifying, that gives us a probability of 1/6 or approximately 0.1667.
Looks like Nathan has a 1 in 6 chance of rolling a sum of 7. Good luck to him!
To calculate the probability of rolling a sum of 7 with two six-sided dice, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes:
To obtain a sum of 7, we need to find all the possible combinations of two numbers that add up to 7. These combinations are: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). So, there are 6 favorable outcomes.
Step 2: Determine the total number of possible outcomes:
Each die has 6 sides with numbers from 1 to 6. Thus, the total number of possible outcomes is the product of the number of sides on each die, which is 6 * 6 = 36.
Step 3: Calculate the probability:
The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.
So, the probability of rolling a sum of 7 is 6/36, which simplifies to 1/6 or approximately 0.1667.
Therefore, the probability that Nathan will roll a sum of 7 is 1/6 or approximately 0.1667.
To find the probability of rolling a sum of 7 with two six-sided dice, we need to determine the number of favorable outcomes and the total number of possible outcomes.
In this case, the favorable outcomes are the combinations of numbers on the red and blue dice that result in a sum of 7. These combinations are: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).
The total number of outcomes is the number of ways the two dice can be rolled. Since each die has six sides, there are 6 possible outcomes on the red die, and for each outcome on the red die, there are 6 possible outcomes on the blue die. Therefore, the total number of outcomes is 6 multiplied by 6, which is 36.
So, the probability of rolling a sum of 7 is the number of favorable outcomes divided by the total number of outcomes.
Number of favorable outcomes = 6
Total number of outcomes = 36
Probability = Number of favorable outcomes / Total number of outcomes
= 6 / 36
= 1 / 6
≈ 0.1667
≈ 16.67%
Thus, the probability that Nathan will roll a sum of 7 is approximately 16.67%.