Final answer:
To find the probability of rolling a sum of 7 with two dice, we determine there are 6 favorable outcomes out of 36 possible when rolling two six-sided dice. Hence, the probability is 6/36, which simplifies to 1/6.
Step-by-step explanation:
The question is asking to find the probability that the sum of the numbers rolled on two fair six-sided dice, one green and one red, is 7. We know that there are 36 possible outcomes when two dice are rolled (6 options for the green die and 6 for the red die, multiplied together). To calculate the probability, we need to find how many of these outcomes result in a sum of 7.
The pairs that give us a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are 6 such combinations. Hence, the probability P(sum of 7) is the number of successful outcomes divided by the total number of possible outcomes, which is 6/36, or simplified to 1/6.
When two fair dice are tossed simultaneously, one green and one red, there are 36 possible outcomes in the sample space. To find the probability that the sum is 7, we need to determine how many of these outcomes result in a sum of 7. There are 6 possible outcomes that result in a sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). Therefore, the probability is 6/36, which simplifies to 1/6.
The probability of rolling a sum of 7 with two dice is therefore 1/6.