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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:

2, 5, 7, 8

She then 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. The probability of getting a sum that is less than 10 is [tex]\(\frac{21}{40}\)[/tex].
D. A sum equal to 8 is the result 20 times in 80 rounds. This suggests the game is unfair.
E. The probability of getting a sum that is greater than or equal to 12 is [tex]\(\frac{11}{86}\)[/tex].

Sagot :

GinnyAnswer
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.
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