Let us break down the problem and verify each statement:
1. Probability of getting a sum that is a multiple of 3:
According to the provided answer, the probability of getting a sum that is a multiple of 3 is 0.375.
2. Probability of getting a sum that is greater than or equal to 12:
The given result indicates that the probability of getting a sum that is greater than or equal to 12 is 0.275.
3. Probability of getting a sum that is even:
The provided result tells us that the probability of getting an even sum is 0.5.
4. Probability of getting a sum that is less than 10:
The given result states that the probability of getting a sum that is less than 10 is 0.525.
5. Sum equal to 8 occurring 20 times in 80 rounds:
The result is 0.25, which indicates that in 80 rounds, the sum equals 8 exactly 20 times. While this alone can't be used to definitively declare the game unfair without further context, the occurrence of 20 out of 80 trials indicates a probability of getting 8 as 0.25.
Then, putting everything together:
True statements are:
- The probability of getting a sum that is a multiple of 3 is [tex]\(\frac{3}{8}\)[/tex].
- The probability of getting a sum that is greater than or equal to 12 is [tex]\(\frac{11}{40}\)[/tex].
- The probability of getting a sum that is even is [tex]\(\frac{1}{2}\)[/tex].
- The probability of getting a sum that is less than 10 is [tex]\(\frac{21}{40}\)[/tex].
- A sum equal to 8 occurs 20 times in 80 rounds.
Therefore, all the given statements are correct, based on the breakdown of the results provided.
