Question

A six-sided number cube is rolled 600 times. The results are 246 even numbers and 354 odd numbers.

How does the relative frequency of rolling an odd number compare to the theoretical probability?

Select from the drop-down menus to correctly complete the statements.

The relative frequency of rolling an odd number is
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the theoretical probability. The theoretical probability is
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and the relative frequency is
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.

Answer 1

To analyze the situation, let's start with the theoretical probability of rolling an odd number on a six-sided die. The odd numbers on a die are 1, 3, and 5, which gives us a total of 3 odd numbers out of 6 possible outcomes.

The theoretical probability (P) of rolling an odd number is calculated as follows:

\[ P(\text{odd}) = \frac{\text{Number of odd outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2} = 0.5 \]

Now, we need to determine the relative frequency of rolling an odd number based on the results of the 600 rolls.

The total number of rolls is 600, and we know that there were 354 odd numbers rolled. The relative frequency (RF) of rolling an odd number is:

\[ RF(\text{odd}) = \frac{\text{Number of odd outcomes}}{\text{Total rolls}} = \frac{354}{600} \]

Now we calculate \( \frac{354}{600} \):

\[ RF(\text{odd}) = 0.59 \]

Now we can compare the relative frequency to the theoretical probability:

1. **The relative frequency of rolling an odd number is** **greater than** **the theoretical probability.**

2. **The theoretical probability is** **0.5** **and the relative frequency is** **0.59.**

So, filling in the drop-down menus, the completed statements would be:

The relative frequency of rolling an odd number is **greater than** the theoretical probability. The theoretical probability is **0.5** and the relative frequency is **0.59**.