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Task 3: Probabilities of interest in two-dice experiments
Task 3: Probabilities of interest in two-dice experiments
Which of the two events, A or B, is more likely?
Likelihood of two events:
- A = {at least one 6 when rolling a single dice 4 times}
- B = {at least one pair 66 when rolling two dice 24 times}
The probability of a 6 in a single roll of a dice is 1/6, so in a long sequence of four rolls, we may expect to see a 6 about 4×(1/6) = 2/3 of time.
Likewise, the probability of a pair 66 in a single roll of two dice is 1/36; hence, in a long sequence of 24 rolls of two dice, we may expect to see 66 about 24×(1/36) = 24/36 = 2/3 of time – the same!
From this consideration, it may seem that events A and B are equally likely.
Is that correct? The subtlety of the question is in the words “at least one”!
The tasks for you are now the following:
- Design and conduct two separate simulations to try and evaluate the probabilities P(A) and P(B) numerically.
Note: Because these probabilities may be expected to be quite close to each other (if not identical), you will need to use quite a lot of replications (perhaps 100,000 or so). - Evaluate the MOE in both simulations, which should provide sufficient confidence (e.g 95%) in discriminating between the two probabilities.
