To solve the problem, let's break it down and analyze each statement:
1. Probability of getting a sum that is even:
- The probability of getting a sum that is even is [tex]\( \frac{1}{2} \)[/tex] or 0.5. After calculation, this statement is true.
2. Probability of getting a sum that is a multiple of 3:
- The probability of getting a sum that is a multiple of 3 is [tex]\( \frac{3}{8} \)[/tex] or 0.375. After calculation, this statement is true.
3. Probability of getting a sum equal to 8:
- The statement says that in 80 rounds, the sum is equal to 8 in 20 of those rounds.
- The fraction [tex]\( \frac{20}{80} \)[/tex] simplifies to [tex]\( \frac{1}{4} \)[/tex] or 0.25 indicating the probability.
- The statement "This suggests the game is unfair" is not necessarily true unless further context on fairness or expected probability is given.
- The probability of getting a sum equal to 8 is indeed [tex]\( \frac{1}{4} \)[/tex] or 0.25. This part of the statement is true, but the suggestion of the game being unfair is outside the scope of the given information.
4. Probability of getting a sum that is greater than or equal to 12:
- The probability of getting a sum that is greater or equal to 12 is [tex]\( \frac{11}{40} \)[/tex] or 0.275. After calculation, this statement is true.
5. Probability of getting a sum that is less than 10:
- The probability of getting a sum that is less than 10 is [tex]\( \frac{21}{40} \)[/tex] or 0.525. After calculation, this statement is true.
Therefore, the true statements based on the calculations are all of them:
- The probability of getting a sum that is even is [tex]\( \frac{1}{2} \)[/tex].
- The probability of getting a sum that is a multiple of 3 is [tex]\( \frac{3}{8} \)[/tex].
- The probability of getting a sum equal to 8 is [tex]\( \frac{1}{4} \)[/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 less than 10 is [tex]\( \frac{21}{40} \)[/tex].
