Question

Determine the probability of getting 6 or 7 in a toss of two dice.

Short answer

The probability of getting a sum of 6 or 7 in a toss of two dice is \(P(6 \textrm{ or } 7) = \frac{11}{36}\).

Step-by-step solution

Determine the total possible outcomes

When rolling two dice, there are 6 sides on each die, which means there are a total of 6 x 6 = 36 possible combinations of outcomes.

Identify the successful outcomes for both 6 and 7

We need to find the combinations of the dice rolls that result in a sum of either 6 or 7. Combinations for 6 are: (1,5), (2,4), (3,3), (4,2), (5,1) - 5 combinations Combinations for 7 are: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) - 6 combinations

Calculate the total successful outcomes

We now add the number of successful outcomes for 6 and 7. There are 5 combinations for 6 and 6 combinations for 7, so in total, there are 5 + 6 = 11 successful outcomes.

Calculate the probability

Now we can determine the probability by dividing the number of successful outcomes by the total possible outcomes. Probability (P) = Successful outcomes / Total possible outcomes = 11/36 So, \(P(6 \textrm{ or } 7) = \frac{11}{36}\).