To calculate the theoretical probability of rolling a 7 or 11 on a pair of number cubes, we first need to determine all the possible outcomes of rolling two dice.
There are 6 possible outcomes for each dice, so the total number of outcomes for rolling two dice is 6^2 = 36.
Next, we need to find the number of outcomes that result in a sum of 7 or 11:
- For a sum of 7: There are 6 ways to roll a 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).
- For a sum of 11: There are only 2 ways to roll an 11 (5+6, 6+5).
Therefore, the total number of favorable outcomes is 6 + 2 = 8.
Finally, we can calculate the theoretical probability of rolling a 7 or 11 on a pair of number cubes by dividing the number of favorable outcomes by the total number of outcomes:
P(7 or 11) = Number of favorable outcomes / Total number of outcomes
P(7 or 11) = 8 / 36
P(7 or 11) = 2 / 9
So, the theoretical probability of rolling a 7 or 11 on a pair of number cubes from a single toss is 2/9 or approximately 0.2222 (22.22%).
calculate the theatrical probability of rolling of 7 or 11 on a pair of number cubes from a single toss
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