Calculate the theoretical probability of rolling a total of 7 or 11 on a pair of number cubes from a single toss.(1 point) P(7 or 11)=
To find the theoretical probability of rolling a total of 7 or 11 on a pair of number cubes, we need to first find all the possible outcomes when rolling two number cubes.
There are 6 sides on each cube, so the total number of outcomes when rolling two cubes is 6 x 6 = 36.
Next, we need to determine the outcomes that result in a total of 7 or 11 when adding the numbers on the two cubes:
For total of 7:
(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
There are a total of 6 outcomes that result in a total of 7.
For total of 11:
(5,6), (6,5)
There are a total of 2 outcomes that result in a total of 11.
Therefore, the total number of outcomes that result in a total of 7 or 11 is 6 (total of 7) + 2 (total of 11) = 8.
To calculate the theoretical probability of rolling a total of 7 or 11:
P(7 or 11) = Number of favorable outcomes / Total number of possible outcomes
P(7 or 11) = 8 / 36
P(7 or 11) = 2 / 9
Therefore, the theoretical probability of rolling a total of 7 or 11 on a pair of number cubes from a single toss is 2/9.