Question

When rolling a pair of dice, the roll should come up 11 once every 18 rolls, or 5.6% of the time. You decide to test this out, rolling 40 times a day every weekday, and using the weekend to analyze the data. As the table shows, with the exception of Friday, every day you rolled either double the expected number of 11s, half the expected number of 11s or no 11s at all. Yet the average for all the days is 5.5%, virtually identical with the theoretical number. How do you explain this?

A) The errors in the four bad trials cancelled each other out.
B) Rolling dice is all luck; probability is simply not involved.
C) Experimental probability approaches theoretical probability when the number of trials is large.
D) Your knowledge of the expected probability influenced the eventual outcome of the experiment, changing the number of 11s you rolled on the last two days.

Answer 1

These dice rolls are independent events and so there is no conditional probability involved. Each event has the same probability, no matter what happened before. Unless there was a constant like a robot rolling the dice a specific way each time, a man rolling a die has too many variables to even suggest probability.

Answer 2

C) Experimental probability approaches theoretical probability when the number of trials is large.

Explanation:

Experimental probability should approach theoretical probability as the number of trials gets larger. Experimental probability is bases on a set of trials and theoretical probability is based on on all possible outcomes.