Two standard number cubes are thrown simultaneously. What is the probability that the combined result of the two cubes is exactly 7, or that it is less than (but not equal to) 6? Round answer to the nearest thousandth
7 = 5,2; 2,5; 3,4; 4,3; 6,1; 1,6 = 6/36
6 < 1,1; 2,2; 1,2; 2,1; 1,3; 3,1; 1,4; 4,1; 2,3; 3,2 = 10/36
Either-or probabilities are found by adding the individual probabilities.
Two standard number cubes are thrown simultaneously. What is the probability that the combined result of the two cubes is exactly 7, or that it is less than (but not equal to) 6? Round answer to the nearest thousandth.
Two standard number cubes are thrown simultaneously. What is the probability that the combined result of the two cubes is exactly 7, or that it is less than (but not equal to) 6? Round answer to the nearest thousandth.
To calculate the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's consider the possible outcomes for each cube. A standard number cube has 6 sides, numbered from 1 to 6.
Now, let's calculate the number of favorable outcomes:
1. To get a combined result of exactly 7, the two cubes can have the following combinations: {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}. So, we have 6 favorable outcomes for this case.
2. To get a combined result that's less than 6, we need to consider {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)}. So, we have 15 favorable outcomes for this case.
Next, let's calculate the total number of possible outcomes. Since each cube has 6 possible outcomes, the total number of possible outcomes when two cubes are thrown simultaneously is 6 x 6 = 36.
Now, let's calculate the probability:
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
For the first case (combined result of 7), the probability is 6/36 = 1/6.
For the second case (combined result less than 6), the probability is 15/36 = 5/12.
To find the probability that the combined result is either 7 or less than 6, we need to sum up the probabilities of both cases:
Probability = Probability of (combined result of 7) + Probability of (combined result less than 6)
Probability = 1/6 + 5/12 = 2/12 + 5/12 = 7/12
Therefore, the probability that the combined result of the two cubes is exactly 7 or less than 6 is 7/12, rounded to the nearest thousandth.