Final answer:
The probability of getting at least one 6 and a total score of 7 with two dice is 1/36, as there is only one combination (a 6 and a 1) out of the 36 possible that fulfillsboth criteria.
Step-by-step explanation:
To find the probability of throwing at least one 6 and a total score of 7 when two fair, six-sided dice are rolled, you need to consider the possible combinations that could result in this specific outcome. There is only one combination that fulfills both criteria, which is when the first die shows a 6 and the second die shows a 1. The total number of possible outcomes when rolling two dice is 6 x 6 = 36, so the sample space for two six-sided dice has 36 outcomes. Given this, the probability of rolling a 6 on the first die is 1/6, and the probability of rolling a 1 on the second die is also 1/6.
To find the combined probability for both dice, you multiply the probabilities together:
- Probability of rolling one 6 (on either die) = 1/6
- Probability of rolling a 1 (on the other die) = 1/6
- Combined probability = (1/6) x (1/6) = 1/36
Therefore, the probability of getting at least one 6 and a score of 7 with a pair of dice is 1/36.