Question
Danielle makes fluffy stuffed animals to give to local charities. She has a container of 500 googly eyes in different sizes that she sews onto the animals. She randomly selects 28 googly eyes from the container and gets 12 small, 9 medium, and 7 large eyes.
Based on the data, what is the probability that the next googly eye Danielle selects will be large?
Write your answer as a fraction or whole number.
Based on the data, what is the probability that the next googly eye Danielle selects will be large?
Write your answer as a fraction or whole number.
Answers
Answered by
GPT-4o mini
To find the probability that the next googly eye Danielle selects will be large, we first need to determine the total number of googly eyes she has in the container and the number of large googly eyes available.
From the problem, we know that Danielle has a total of 500 googly eyes. Out of the 28 googly eyes she selected, she received:
- 12 small eyes
- 9 medium eyes
- 7 large eyes
Now, to find the total number of large googly eyes remaining in the container, we can start with the total number of googly eyes (500) and subtract the number she has already selected (28).
Total googly eyes remaining = 500 - 28 = 472.
Next, we need to determine how many large googly eyes are left. Initially, we do not have the exact counts of how many large eyes were in the container, but we know that she selected 7 large eyes from the random draw of 28.
Since large googly eyes are among the total available, let's denote:
- \( L \) = total number of large googly eyes in the container before selection
Thus after selecting 7 large eyes, the number of large googly eyes remaining is \( L - 7 \).
To find the total number of googly eyes remaining (472), we can express the total number of googly eyes as follows:
- Total remaining = (Remaining small eyes) + (Remaining medium eyes) + (Remaining large eyes)
- We do not know exactly how many small and medium eyes were initially in the container, but we do know the total types of eyes selected, implying that there are still several eyes of each type left.
The probability of selecting a large googly eye next is calculated by finding:
\[
\text{Probability (next googly eye is large)} = \frac{\text{Remaining large eyes}}{\text{Total remaining eyes}}
= \frac{L - 7}{472}
\]
Without knowing \( L \) (the total number of large googly eyes originally in the container), we cannot calculate the exact number. However, we can still note that the formula for probability will guide us once \( L \) or the ratio between the types of eyes is established.
To illustrate, say if approximately 20% of the eyes were large initially, it would imply:
\( L \) could be around \( 500 \times 0.2 = 100 \) (Large).
Then, it would lead to \( \frac{100 - 7}{472} = \frac{93}{472} \) if \( L = 100 \).
Finally with the available information and calculations, it's key to note that we need more data about the initial splits among different eyes in the container to derive the exact numeric probability. However, the formula setup is as follows:
\[
\frac{L - 7}{472}
\] is the structured way of expressing probability until the specific number \( L \) is known.
To succinctly finish, if one could ascertain \( L \) or proportions from initial conditions, plugging it in would yield the final probability clearly. Thus we're obtaining a general sense of how to approach probability with the information given.
From the problem, we know that Danielle has a total of 500 googly eyes. Out of the 28 googly eyes she selected, she received:
- 12 small eyes
- 9 medium eyes
- 7 large eyes
Now, to find the total number of large googly eyes remaining in the container, we can start with the total number of googly eyes (500) and subtract the number she has already selected (28).
Total googly eyes remaining = 500 - 28 = 472.
Next, we need to determine how many large googly eyes are left. Initially, we do not have the exact counts of how many large eyes were in the container, but we know that she selected 7 large eyes from the random draw of 28.
Since large googly eyes are among the total available, let's denote:
- \( L \) = total number of large googly eyes in the container before selection
Thus after selecting 7 large eyes, the number of large googly eyes remaining is \( L - 7 \).
To find the total number of googly eyes remaining (472), we can express the total number of googly eyes as follows:
- Total remaining = (Remaining small eyes) + (Remaining medium eyes) + (Remaining large eyes)
- We do not know exactly how many small and medium eyes were initially in the container, but we do know the total types of eyes selected, implying that there are still several eyes of each type left.
The probability of selecting a large googly eye next is calculated by finding:
\[
\text{Probability (next googly eye is large)} = \frac{\text{Remaining large eyes}}{\text{Total remaining eyes}}
= \frac{L - 7}{472}
\]
Without knowing \( L \) (the total number of large googly eyes originally in the container), we cannot calculate the exact number. However, we can still note that the formula for probability will guide us once \( L \) or the ratio between the types of eyes is established.
To illustrate, say if approximately 20% of the eyes were large initially, it would imply:
\( L \) could be around \( 500 \times 0.2 = 100 \) (Large).
Then, it would lead to \( \frac{100 - 7}{472} = \frac{93}{472} \) if \( L = 100 \).
Finally with the available information and calculations, it's key to note that we need more data about the initial splits among different eyes in the container to derive the exact numeric probability. However, the formula setup is as follows:
\[
\frac{L - 7}{472}
\] is the structured way of expressing probability until the specific number \( L \) is known.
To succinctly finish, if one could ascertain \( L \) or proportions from initial conditions, plugging it in would yield the final probability clearly. Thus we're obtaining a general sense of how to approach probability with the information given.