You roll a six sided die 8 times. You get the number 5 only once. And so you conclude that P(5) = 1/8. What type of probability is illustrated and why?
This is an example of empirical probability because it is based on observed or experimental data. The probability of rolling a 5 is calculated by dividing the number of times a 5 was observed by the total number of times the die was rolled. In this case, a 5 was observed once out of 8 rolls, leading to a probability of 1/8.
The type of probability illustrated in this scenario is a classical probability.
Classical probability is based on the assumption that all outcomes are equally likely. In this case, since you are rolling a fair six-sided die, each number (1, 2, 3, 4, 5, or 6) has an equal probability of occurring.
Therefore, the probability of rolling a 5 on any given roll is 1/6. However, the fact that you rolled the number 5 only once in 8 rolls does not change the probability of rolling a 5 on any single roll. The probability of rolling a 5 on any single roll remains 1/6, and it is not affected by previous outcomes.
So, concluding that P(5) = 1/8 in this scenario is incorrect because it assumes that all outcomes have an equal probability, which is not the case for rolling a die.