Question
If Talia spins a spinner with 26 equal spaces (labeled A to Z), what is the theoretical probability that she lands on any letter in the word “Mississippi”?(1 point)
Responses
213
Start Fraction 2 over 13 End Fraction
23
Start Fraction 2 over 3 End Fraction
16
Start Fraction 1 over 6 End Fraction
313
Sadiq rolls a regular six-sided number cube 10 times and gets an even number 7 times. How does his experimental probability compare to the theoretical probability?(1 point)
Responses
The experimental probability was greater than the theoretical probability.
The experimental probability was greater than the theoretical probability.
The theoretical probability is greater than the experimental probability.
The theoretical probability is greater than the experimental probability.
The experimental and theoretical probability are equal.
The experimental and theoretical probability are equal.
The theoretical and experimental probabilities are opposites.
The theoretical and experimental probabilities are opposites.
Question
You are rolling a number cube to help you pick the number of minutes you will run in each of your workout sets. Determine the probability of rolling an odd number three times in a row.(1 point)
Responses
1216
Start Fraction 1 over 216 End Fraction
18
Start Fraction 1 over 8 End Fraction
12
Start Fraction 1 over 2 End Fraction
32
Which of the following shows the correct calculation for finding the probability of rolling two number cubes and getting a sum of 6 or 11?(1 point)
Responses
636 +236
Start Fraction 6 over 36 End Fraction plus Start Fraction 2 over 36 End Fraction
636 ⋅236
Start Fraction 6 over 36 End Fraction times Start Fraction 2 over 36 End Fraction
536 +236
Start Fraction 5 over 36 End Fraction plus Start Fraction 2 over 36 End Fraction
536 ⋅236
Responses
213
Start Fraction 2 over 13 End Fraction
23
Start Fraction 2 over 3 End Fraction
16
Start Fraction 1 over 6 End Fraction
313
Sadiq rolls a regular six-sided number cube 10 times and gets an even number 7 times. How does his experimental probability compare to the theoretical probability?(1 point)
Responses
The experimental probability was greater than the theoretical probability.
The experimental probability was greater than the theoretical probability.
The theoretical probability is greater than the experimental probability.
The theoretical probability is greater than the experimental probability.
The experimental and theoretical probability are equal.
The experimental and theoretical probability are equal.
The theoretical and experimental probabilities are opposites.
The theoretical and experimental probabilities are opposites.
Question
You are rolling a number cube to help you pick the number of minutes you will run in each of your workout sets. Determine the probability of rolling an odd number three times in a row.(1 point)
Responses
1216
Start Fraction 1 over 216 End Fraction
18
Start Fraction 1 over 8 End Fraction
12
Start Fraction 1 over 2 End Fraction
32
Which of the following shows the correct calculation for finding the probability of rolling two number cubes and getting a sum of 6 or 11?(1 point)
Responses
636 +236
Start Fraction 6 over 36 End Fraction plus Start Fraction 2 over 36 End Fraction
636 ⋅236
Start Fraction 6 over 36 End Fraction times Start Fraction 2 over 36 End Fraction
536 +236
Start Fraction 5 over 36 End Fraction plus Start Fraction 2 over 36 End Fraction
536 ⋅236
Answers
GPT-4o mini
Let’s analyze each question one at a time:
1. **Theoretical probability of landing on any letter in the word "Mississippi":**
- The word "Mississippi" has the letters: M, i, s, s, i, s, s, i, p, p, which includes the letters M (1), i (4), s (4), p (2).
- The total number of letters is 11.
- There are 4 unique letters (M, i, s, p) in "Mississippi".
- Therefore, the probability of landing on any of these letters is \( \frac{11}{26} \).
- The words "Mississippi" has 4 letters that can appear (M, I, S, P) for a total of 11 letters. Thus, the probability for selecting any letter from the word is calculated using:
\[
P = \frac{4}{26} = \frac{2}{13}
\]
**Answer:** \( \frac{2}{13} \)
2. **Sadiq's experimental probability vs. theoretical probability:**
- The theoretical probability of rolling an even number on a six-sided die is \( \frac{3}{6} = \frac{1}{2} \).
- Sadiq rolled an even number 7 times out of 10 trials, so his experimental probability is \( \frac{7}{10} \).
- Comparing the experimental probability \( \frac{7}{10} = 0.7 \) to the theoretical probability \( \frac{1}{2} = 0.5 \):
- \( \frac{7}{10} > \frac{1}{2} \)
- Therefore, the experimental probability was greater than the theoretical probability.
**Answer:** The experimental probability was greater than the theoretical probability.
3. **Probability of rolling an odd number three times in a row:**
- The probability of rolling an odd number (1, 3, 5) on a six-sided die is \( \frac{3}{6} = \frac{1}{2} \).
- Since rolls are independent, we multiply the probabilities:
\[
P(odd) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{8}
\]
**Answer:** \( \frac{1}{8} \)
4. **Calculating the probability of rolling two number cubes and getting a sum of 6 or 11:**
- To find the probability of getting a sum of 6, there are several combinations:
- (1,5), (2,4), (3,3), (4,2), (5,1) = 5 ways
- For a sum of 11, the combinations are:
- (5,6), (6,5) = 2 ways
- Therefore, total outcomes for sums of 6 or 11 = 5 + 2 = 7 ways.
- As there are 36 possible outcomes when rolling two dice (6 sides each), the calculation for the probability of getting a sum of 6 or 11 is:
\[
P = \frac{7}{36}
\]
**Answer:** \( \frac{5}{36} + \frac{2}{36} \) which simplifies to \( \frac{7}{36} \).
To summarize, here are all the corresponding answers:
1. \( \frac{2}{13} \)
2. The experimental probability was greater than the theoretical probability.
3. \( \frac{1}{8} \)
4. \( \frac{5}{36} + \frac{2}{36} \) (this would be option corresponding to sum of 6 or 11).
1. **Theoretical probability of landing on any letter in the word "Mississippi":**
- The word "Mississippi" has the letters: M, i, s, s, i, s, s, i, p, p, which includes the letters M (1), i (4), s (4), p (2).
- The total number of letters is 11.
- There are 4 unique letters (M, i, s, p) in "Mississippi".
- Therefore, the probability of landing on any of these letters is \( \frac{11}{26} \).
- The words "Mississippi" has 4 letters that can appear (M, I, S, P) for a total of 11 letters. Thus, the probability for selecting any letter from the word is calculated using:
\[
P = \frac{4}{26} = \frac{2}{13}
\]
**Answer:** \( \frac{2}{13} \)
2. **Sadiq's experimental probability vs. theoretical probability:**
- The theoretical probability of rolling an even number on a six-sided die is \( \frac{3}{6} = \frac{1}{2} \).
- Sadiq rolled an even number 7 times out of 10 trials, so his experimental probability is \( \frac{7}{10} \).
- Comparing the experimental probability \( \frac{7}{10} = 0.7 \) to the theoretical probability \( \frac{1}{2} = 0.5 \):
- \( \frac{7}{10} > \frac{1}{2} \)
- Therefore, the experimental probability was greater than the theoretical probability.
**Answer:** The experimental probability was greater than the theoretical probability.
3. **Probability of rolling an odd number three times in a row:**
- The probability of rolling an odd number (1, 3, 5) on a six-sided die is \( \frac{3}{6} = \frac{1}{2} \).
- Since rolls are independent, we multiply the probabilities:
\[
P(odd) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{8}
\]
**Answer:** \( \frac{1}{8} \)
4. **Calculating the probability of rolling two number cubes and getting a sum of 6 or 11:**
- To find the probability of getting a sum of 6, there are several combinations:
- (1,5), (2,4), (3,3), (4,2), (5,1) = 5 ways
- For a sum of 11, the combinations are:
- (5,6), (6,5) = 2 ways
- Therefore, total outcomes for sums of 6 or 11 = 5 + 2 = 7 ways.
- As there are 36 possible outcomes when rolling two dice (6 sides each), the calculation for the probability of getting a sum of 6 or 11 is:
\[
P = \frac{7}{36}
\]
**Answer:** \( \frac{5}{36} + \frac{2}{36} \) which simplifies to \( \frac{7}{36} \).
To summarize, here are all the corresponding answers:
1. \( \frac{2}{13} \)
2. The experimental probability was greater than the theoretical probability.
3. \( \frac{1}{8} \)
4. \( \frac{5}{36} + \frac{2}{36} \) (this would be option corresponding to sum of 6 or 11).