There is a number cube with faces numbered 1 to 6. There is also a coin with one side marked as heads and the other tails.
As a trial of an experiment, the number cube was rolled and the coin flipped. The number (1 to 6) from the roll and the side (H for heads and T for talls) of
the coin from the flip were recorded.
Here is a summary of the data from 1050 trials.
Outcome 1H 2H 3H 4H 5H 6H 1T 2T 3T 4T 5T 6T
Number of trials 79 99 89 88 89 96 92 86 97 79 77 79
Answer each part.
(a) Assuming the cube and the coin are fair, find the theoretical probability of this event: both
rolling a 1 ora 6 and flipping tails, in a single trial. Round your answer to the nearest
thousandth.
0
(b) Use the data to find the experimental probability of this event: both rolling a 1 or a 6 and
nipping talls, in a single trial. Round your answer to the nearest thousandth.
0
(c) Choose the statement that is true.
With a large number of trials, there might be a difference between the experimental
and theoretical probabilities, but the difference should be small.
With a large number of trials, there must be a large difference between the
experimental and theoretical probabilities.
With a large number of trials, there must be no difference between the experimental
and theoretical probabilities.
5