Answer:
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.
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:
[tex]\mathbf{P(2) = \frac{1}{12}}\\[/tex]
Express as decimals
[tex]\mathbf{P(2) = 0.083}[/tex]
The experimental probability of 2 in after 200 rolls is:
[tex]\mathbf{P(2) = \frac{18}{200}}[/tex]
Express as decimals
[tex]\mathbf{P(2) = 0.09}[/tex]
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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