Sure, let's analyze each statement and verify its correctness based on the given probability results:
1. The probability of getting a sum that is even is [tex]\(\frac{1}{2}\)[/tex]:
- According to the given probability results, the probability of getting an even sum is 0.5.
- Converting 0.5 to a fraction, we get [tex]\(\frac{1}{2}\)[/tex].
- Therefore, this statement is true.
2. The probability of getting a sum that is a multiple of 3 is [tex]\(\frac{3}{8}\)[/tex]:
- The given probability of getting a sum that is a multiple of 3 is 0.375.
- Converting 0.375 to a fraction, we get [tex]\(\frac{3}{8}\)[/tex].
- Therefore, this statement is true.
3. The probability of getting a sum that is less than 10 is [tex]\(\frac{21}{40}\)[/tex]:
- The given probability of getting a sum that is less than 10 is 0.4375.
- Converting 0.4375 to a fraction, we get [tex]\(\frac{21}{40}\)[/tex].
- Therefore, this statement is true.
4. A sum equal to 8 is the result 20 times in 80 rounds. This suggests the game is unfair:
- The given number of expected occurrences of a sum equal to 8 in 80 rounds is 7.5.
- Since 7.5 is far from 20, the statement that a sum equal to 8 occurs 20 times in 80 rounds suggests an anomaly.
- Therefore, this statement is true in highlighting a discrepancy.
5. The probability of getting a sum that is greater than or equal to 12 is [tex]\(\frac{11}{86}\)[/tex]:
- The given probability of getting a sum greater than or equal to 12 is 0.34375.
- Converting 0.34375 to a fraction, we get [tex]\(\frac{11}{32}\)[/tex], not [tex]\(\frac{11}{86}\)[/tex].
- Therefore, this statement is false.
So, the true statements are:
- 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 that is less than 10 is [tex]\(\frac{21}{40}\)[/tex].
- A sum equal to 8 is the result 20 times in 80 rounds. This suggests the game is unfair.
