1. You roll a number cube numbered one to six 12 times. P(5)=2/3. What type of probability is illustrated and why?
A. Experimental; the result is based on the number of possible outcomes.
B. Experimental; the result is found by repeating an experiment.
C. Theoretical; the result is based on the number of outcomes.**********?
D. Theoretical; the result is found by repeating an experiment.
6 possible outcomes
only 1 is a 5
So, theoretical P(5) = 1/6
You rolled 12 times, so that's B: experimentation. Evidently the die was heavily loaded.
The correct answer is C. Theoretical; the result is based on the number of outcomes.
To explain further, let's break down the question:
You are rolling a number cube, which has six sides numbered one to six. This means that there are six possible outcomes when rolling the cube.
You rolled the number cube 12 times, and the probability of getting a 5 is given as 2/3.
In this scenario, experimental probability would involve conducting the experiment (rolling the cube) repeatedly and calculating the probability based on the observed results. However, the question states that the probability is given as 2/3, which means it is not based on observed outcomes but rather on a given probability value.
Theoretical probability, on the other hand, is based on the number of possible outcomes. Since the cube has six sides and each side has an equal chance of being rolled, the probability of rolling a 5 is 1/6. Therefore, the given probability of 2/3 does not match the theoretical probability, making C the correct answer.