Question

You suspect a 6-sided die to be loaded and conduct a probability experiment by rolling the die 400 ×. Do you think the die is loaded?

a) No, because each value has an approximately equal chance of occurring.
b) Yes, because the probabilities are not the same.
c) Yes, because two of the values have a higher probability of occurring than expected under the assumption of equally likely outcomes.

Answer 1

To suspect a die is loaded, observed frequencies after a significant number of rolls should deviate substantially from the expected frequency of 1/6 for each number. If two numbers appear more frequently in a pattern that differs significantly from the expected frequency, the die may be loaded.

Step-by-step explanation:

To determine if you suspect a 6-sided die to be loaded after conducting a probability experiment by rolling the die 400 times, you'd need to analyze the outcomes. If the die is fair, the expected frequency of each number (1 through 6) should be roughly equal, or near 1/6 of the total rolls. That means each number should appear approximately 66 or 67 times out of 400 rolls (400/6 ≈ 66.67). If you observe that two numbers appear significantly more frequently than this, option c) may be correct, indicating that the die is likely loaded because two of the values have a higher probability than the others.

For a fair die, the theoretical probability of each number coming up is 1/6. However, in practice, slight deviations are normal. If the deviation is large or consistent across several trials, this suggests an unfair or loaded die. You said two numbers have a higher probability; if this is based on significant statistical deviation from the expected frequencies, then yes, it is reasonable to suspect that the die is loaded.