The probability of rolling two 3s with a fair number cube is:
P(rolling two 3s) = P(rolling a 3 on the first roll) x P(rolling a 3 on the second roll)
P(rolling two 3s) = (1/6) x (1/6) = 1/36
This is the theoretical probability of rolling two 3s.
The experimental probability of rolling two 3s after 500 trials is 11/50. We can use this value to estimate the actual number of outcomes:
Number of actual outcomes = Experimental probability x Number of trials
Number of actual outcomes = (11/50) x 500 = 110
The expected number of outcomes can be calculated using the theoretical probability:
Number of expected outcomes = Theoretical probability x Number of trials
Number of expected outcomes = (1/36) x 500 = 13.89
The difference between the number of expected outcomes and the number of actual outcomes is:
Difference = Number of actual outcomes - Number of expected outcomes
Difference = 110 - 13.89
Difference = 96.11
Therefore, the difference between the number of expected outcomes and the number of actual outcomes is approximately 96.11.