Martha wants to investigate whether her 12-sided number cube is fair. In the first 10 rolls of the number cube, the number 2 was rolled 4 times. After rolling the number cube 200 times, 2 was rolled 18 times. Which statement regarding the probability of rolling a 2 on this 12-sided number cube is true?

We can conclude that the 12-sided number cube is fair

The given parameters are:

The theoretical probability of 2 in a 12-sided number cube is:

Express as decimals

The experimental probability of 2 in after 200 rolls is:

Express as decimals

By comparing the experimental and the theoretical probabilities, we can see that: 0.08 and 0.09

Hence, we can conclude that the 12-sided number cube is fair

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The number cube as 12 sides, and if it is fair, then each one of the 12 numbers should have the same probability of being rolled.

This means that the probability of rolling a 2 should be equal to 1/12 = 0.0833

Remember that this is theoretical, we should expect to see this probability with a really high number of rolls.

On the first experiment, there were 10 rolls, and the number 2 showed up 4 times, then based on this, the relative frequency is equal to the quotient of the number of times that the 2 was rolled (4) and the total number of rolls

p = 4/10 = 0.4

This differs with the theoretical probability, we should expect that as we increment the number of rolls, the experimental probability should approximate to the theoretical one.

In the second experiment, we have 200 rolls, and the 2 was rolled 18 times. Then the experimental probability of rolling a 2 is:

p = 18/200 = 0.09

This is almost the same as the theoretical one.

Then we could conclude that the probability of rolling a 2 seems to be the one of fair dice.

t hope this

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