Question

Mary rolled a number cube 40 times and got the following results.Outcome Rolled 1, 2, 3, 4, 5, 6Number of Rolls 9, 9, 10, 3, 6, 3Fill in the table below. Round your answers to the nearest thousandth.(a)Assuming that the cube is fair, compute the theoretical probability of rolling an even number.(b)From Mary's results, compute the experimental probability of rolling an even number.(c)Assuming that the cube is fair, choose the statement below that is true:With a large number of rolls, there must be no difference between the experimental and theoretical probabilities.With a large number of rolls, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.With a large number of rolls, there must be a large difference between the experimental and theoretical probabilities.

Answer 1

a)

The outcomes of rolling a cube can be 1, 2, 3, 4, 5 or 6. From those outcomes, 2, 4 and 6 are even numbers. Then, 3 out of 6 outcomes are even numbers. The theoretical probability of getting an even number is:

`(3)/(6)=(1)/(2)=0.500`

b)

From Mary's results, we can see that a 2 was rolled 9 times, a 4 was rolled 3 times and a 6 was rolled 3 times. The total amount of times that an even number was rolled, is 15. Then, the experimental probability of rolling an even number according to Mary's results, is:

`(15)/(40)=(3)/(8)=0.375`

c)

With a large number of trials, the experimental probability approaches the theoretical probability. Then, with a large number of rolls, there might be a difference between the experimental an theoretical probabilities, but the difference should be small.

Therefore, the answers are:

a) Theoretical probability of rolling an even number: 0.500

b) Experimental probability of rolling an even number: 0.375

c) With a large number of rolls, there might be a difference between the experimental an theoretical probabilities, but the difference should be small.