Question

)A six-sided number cube labeled 1 through 6 is rolled 200 times. An even number is rolled 115 times. Compare the theoretical probability of rolling an even number with the relative frequency of rolling an even number and select one of the statements below that best describes the situation.

The theoretical probability and relative frequency are the same.

The theoretical probability is larger than the relative frequency.

The theoretical probability is smaller than the relative frequency.

There is not enough information to determine the relative frequency.

Answer 1

Answer: The theoretical probability is smaller than the relative frequency.

Explanation:

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Answer 2

`rel.freq= (Successes)/(Total)`

And replacing we got:

`rel.freq= (115)/(200)= 0.575`

The thoeretical probability for this case would be:

`p =(3)/(6)= 0.5`

And the reason of this is because we have 3 even numbers in the total of 6 numbers for a fair dice.

Then we can conclude that the theorical probability would be less than the relative frequency (because 0.5<0.525) and the correct option would be:

The theoretical probability is smaller than the relative frequency.

Explanation:

For this case after 200 times we got an even number 115 times and the relative frequency is given by:

`rel.freq= (Successes)/(Total)`

And replacing we got:

`rel.freq= (115)/(200)= 0.575`

The thoeretical probability for this case would be:

`p =(3)/(6)= 0.5`

And the reason of this is because we have 3 even numbers in the total of 6 numbers for a fair dice.

Then we can conclude that the theorical probability would be less than the relative frequency (because 0.5<0.525) and the correct option would be:

The theoretical probability is smaller than the relative frequency.