Question
Question
Ivan made ice cream pops shown for his family. The white ones were white chocolate. The colored ones were fruit flavors. All of them had sprinkles.
2 white choc and the rest were colored
Select all true statements.
Responses
If Ivan makes
identical batches,
will have sprinkles.
If Ivan makes 10 identical batches, 110 will have sprinkles.
If Ivan makes
identical batches,
will not have sprinkles.
If Ivan makes 10 identical batches, 0 will not have sprinkles.
The probability of getting a fruit flavored ice cream pop is
.
The probability of getting a fruit flavored ice cream pop is 5 sixths.
The probability of getting a fruit flavored ice cream pop is
.
The probability of getting a fruit flavored ice cream pop is 9 over 11.
If Ivan makes
identical batches,
will be white chocolate.
If Ivan makes 10 identical batches, 10 will be white chocolate.
If Ivan makes
identical batches,
will be white chocolate.
If Ivan makes 10 identical batches, 20 will be white chocolate.
The probability of getting a white chocolate ice cream pop is
.
The probability of getting a white chocolate ice cream pop is 1 sixth.
The probability of getting a white chocolate ice cream pop is
.
Answers
Answered by
GPT-4o mini
To analyze the information provided, we first need to clarify the distribution of ice cream pops made by Ivan:
1. **Total Pops**: Ivan made **2 white chocolate pops** and the rest were colored pops. We are not given the total number of pops, but we can infer from the context.
Let’s assume the total number of colored pops is \( x \).
Given that he made a total of \( 2 + x \) pops, the probability calculations will depend on that total.
Based on your statements, let's clarify the truths:
1. **Sprinkles**:
- Every ice cream pop has sprinkles, so it is correct to say that:
- If Ivan makes 10 identical batches (with each batch containing the same number of pops), then all 110 will have sprinkles.
- **True**: "If Ivan makes identical batches, all will have sprinkles."
- **True**: "If Ivan makes 10 identical batches, 110 will have sprinkles."
2. **Not having sprinkles**:
- All pops have sprinkles, so it is false to state that any will not have sprinkles.
- **False**: "If Ivan makes identical batches, 0 will not have sprinkles."
3. **Probability of fruit-flavored pops**:
- If there are 2 white chocolate pops and a total of \( x \) colored pops, the probability of getting a fruit-flavored pop is given by the formula:
\[
P(\text{fruit}) = \frac{\text{Number of colored pops}}{\text{Total number of pops}} = \frac{x}{2+x}
\]
To be true, one of the probabilities must align with known statements.
- The statement "The probability of getting a fruit flavored ice cream pop is 5/6" implies a certain distribution. If \( x = 10 \), then:
\[
P(\text{fruit}) = \frac{10}{2 + 10} = \frac{10}{12} = \frac{5}{6}
\]
Thus, this statement is **True**.
- The statement "The probability of getting a fruit flavored ice cream pop is 9/11" would imply that:
\[
P(\text{fruit}) = \frac{9}{11} \text{ means } x = 9 \text{ and total pops are } 2 + 9 = 11, \text{ which is not true since } 2 = 2.
\]
So, this statement is **False**.
4. **Probability of white chocolate pops**:
- The probability of getting a white chocolate pop:
\[
P(\text{white}) = \frac{\text{Number of white chocolate pops}}{\text{Total number of pops}} = \frac{2}{2+x}
\]
The statement "The probability of getting a white chocolate ice cream pop is 1/6" would need verification.
- If \( P(\text{white}) = \frac{1}{6} \), it implies that:
\[
2 = \frac{1}{6}(2 + x) \Rightarrow 12 = 2 + x \Rightarrow x = 10
\]
This confirms it under the assumption that there are 10 colored pops, making this **True**.
- The last statement provides no contextual value since we calculated based on already known values.
### Summary of True Responses:
1. If Ivan makes identical batches, all will have sprinkles.
2. If Ivan makes 10 identical batches, 110 will have sprinkles.
3. "The probability of getting a fruit flavored ice cream pop is 5/6" is true under certain conditions.
4. "The probability of getting a white chocolate ice cream pop is 1/6" is also true.
Other statements should be marked as false based on the above reasoning.
1. **Total Pops**: Ivan made **2 white chocolate pops** and the rest were colored pops. We are not given the total number of pops, but we can infer from the context.
Let’s assume the total number of colored pops is \( x \).
Given that he made a total of \( 2 + x \) pops, the probability calculations will depend on that total.
Based on your statements, let's clarify the truths:
1. **Sprinkles**:
- Every ice cream pop has sprinkles, so it is correct to say that:
- If Ivan makes 10 identical batches (with each batch containing the same number of pops), then all 110 will have sprinkles.
- **True**: "If Ivan makes identical batches, all will have sprinkles."
- **True**: "If Ivan makes 10 identical batches, 110 will have sprinkles."
2. **Not having sprinkles**:
- All pops have sprinkles, so it is false to state that any will not have sprinkles.
- **False**: "If Ivan makes identical batches, 0 will not have sprinkles."
3. **Probability of fruit-flavored pops**:
- If there are 2 white chocolate pops and a total of \( x \) colored pops, the probability of getting a fruit-flavored pop is given by the formula:
\[
P(\text{fruit}) = \frac{\text{Number of colored pops}}{\text{Total number of pops}} = \frac{x}{2+x}
\]
To be true, one of the probabilities must align with known statements.
- The statement "The probability of getting a fruit flavored ice cream pop is 5/6" implies a certain distribution. If \( x = 10 \), then:
\[
P(\text{fruit}) = \frac{10}{2 + 10} = \frac{10}{12} = \frac{5}{6}
\]
Thus, this statement is **True**.
- The statement "The probability of getting a fruit flavored ice cream pop is 9/11" would imply that:
\[
P(\text{fruit}) = \frac{9}{11} \text{ means } x = 9 \text{ and total pops are } 2 + 9 = 11, \text{ which is not true since } 2 = 2.
\]
So, this statement is **False**.
4. **Probability of white chocolate pops**:
- The probability of getting a white chocolate pop:
\[
P(\text{white}) = \frac{\text{Number of white chocolate pops}}{\text{Total number of pops}} = \frac{2}{2+x}
\]
The statement "The probability of getting a white chocolate ice cream pop is 1/6" would need verification.
- If \( P(\text{white}) = \frac{1}{6} \), it implies that:
\[
2 = \frac{1}{6}(2 + x) \Rightarrow 12 = 2 + x \Rightarrow x = 10
\]
This confirms it under the assumption that there are 10 colored pops, making this **True**.
- The last statement provides no contextual value since we calculated based on already known values.
### Summary of True Responses:
1. If Ivan makes identical batches, all will have sprinkles.
2. If Ivan makes 10 identical batches, 110 will have sprinkles.
3. "The probability of getting a fruit flavored ice cream pop is 5/6" is true under certain conditions.
4. "The probability of getting a white chocolate ice cream pop is 1/6" is also true.
Other statements should be marked as false based on the above reasoning.