Question

sean recorded everyone’s number-cube rolls during the game.
1, 6, 2, 1, 5, 4, 2, 2, 1, 4, 5, 1, 3, 4, 1
he stated that the theoretical probability of rolling a 1 is greater than rolling any other number. explain sean’s error.

Explanation:

1. Theoretical Probability for a Number Cube: A standard number cube (die) has 6 faces numbered 1 - 6. Each face has an equal chance of landing face - up. So the theoretical probability of rolling any specific number (including 1) is calculated as the number of favorable outcomes (1, for rolling a 1) divided by the total number of possible outcomes (6). Mathematically, \(P(1)=\frac{1}{6}\), and the same formula \(P(n)=\frac{1}{6}\) applies to rolling any number \(n\) from 1 to 6. This means that the theoretical probability of rolling a 1 is equal to the theoretical probability of rolling any other number on the cube.
2. Experimental Probability in Sean's Case: Sean's data is from an experiment (recording the rolls of the number - cube during a game). The experimental probability can differ from the theoretical probability, but when considering the theoretical probability (which is based on the nature of the fair number - cube), each number has an equal theoretical probability of being rolled. Sean incorrectly used the experimental results (where 1 might have been rolled more frequently in his game) to make a claim about the theoretical probability.

Answer:

Sean confused theoretical probability with experimental probability.