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Macy rolls a fair, eight-sided die with sides numbered from 1 to 8. Then from a box, she draws a numbered slip of paper. The slips of paper have the numbers shown below. Finally, she calculates the sum of her results.

Select the true statements.

A. The probability of getting a sum that is even is [tex]$\frac{1}{2}$[/tex].
B. The probability of getting a sum that is a multiple of 3 is [tex]$\frac{3}{8}$[/tex].
C. A sum equal to 8 is the result 20 times in 80 rounds. This suggests the game is unfair.
D. The probability of getting a sum that is greater than or equal to 12 is [tex]$\frac{11}{40}$[/tex].
E. The probability of getting a sum that is less than 10 is [tex]$\frac{21}{40}$[/tex].

Sagot :

GinnyAnswer
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].
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