Question

drawing conclusions

1. you roll a six - sided die 60 times. the table shows the results. for which number on the die below is the experimental probability of rolling the number the same as the theoretical probability. (see example 4)

six - sided die results

Explanation:

Step1: Recall Theoretical Probability

For a fair six - sided die, the theoretical probability of rolling any specific number \(n\) (where \(n = 1,2,3,4,5,6\)) is \(P_{theoretical}=\frac{1}{6}\). When rolling the die \(N = 60\) times, the expected number of times we roll a specific number according to theoretical probability is \(E=N\times\frac{1}{6}=60\times\frac{1}{6} = 10\).

Step2: Calculate Experimental Probability for Each Number

• For the number with 1 dot (let's say it represents 1): The number of times it was rolled is 11. The experimental probability - related count is 11, which is not equal to 10.
• For the number with 2 dots (represents 2): The number of times it was rolled is 14, not equal to 10.
• For the number with 3 dots (represents 3): The number of times it was rolled is 7, not equal to 10.
• For the number with 4 dots (represents 4): The number of times it was rolled is 10. This matches the expected number of 10 from theoretical probability.
• For the number with 5 dots (represents 5): The number of times it was rolled is 6, not equal to 10.
• For the number with 6 dots (represents 6): The number of times it was rolled is 12, not equal to 10.

Answer:

The number on the die with 4 dots (the one with four dots, corresponding to the count of 10 in the table) has the experimental probability (in terms of the number of rolls) equal to the theoretical probability - based expected number of rolls. So the number is 4 (the die face with 4 dots, or the one with a count of 10 in the table).