Calculate the theoretical probability of rolling a total of 7 or 11 on a pair of number cubes from a single toss.
P(7 or 11)= ?
To calculate the theoretical probability of rolling a total of 7 or 11 on a pair of number cubes from a single toss, we first need to determine all the possible outcomes when rolling two number cubes.
There are a total of 36 possible outcomes when rolling two number cubes, as each cube has 6 faces and there are 6 * 6 = 36 unique combinations.
Out of the 36 possible outcomes, there are 6 ways to roll a total of 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) and 2 ways to roll a total of 11 (5+6, 6+5).
Therefore, the total number of favorable outcomes is 6 + 2 = 8.
So, the theoretical probability of rolling a total of 7 or 11 on a pair of number cubes from a single toss is:
P(7 or 11) = Number of favorable outcomes / Total number of 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.