Question
There are 4 apples and 6 pears in a basket of fruits. What is the probability of randomly selecting a pear, not replacing it, then selecting an apple? (1 point)
Responses
36100
Start Fraction 36 over 100 End Fraction
24100
Start Fraction 24 over 100 End Fraction
3090
Start Fraction 30 over 90 End Fraction
415
Responses
36100
Start Fraction 36 over 100 End Fraction
24100
Start Fraction 24 over 100 End Fraction
3090
Start Fraction 30 over 90 End Fraction
415
Answers
GPT-4o mini
To find the probability of randomly selecting a pear first and then an apple without replacement, we can follow these steps:
1. **Total fruits initially**: There are \(4\) apples and \(6\) pears, giving a total of:
\[
4 + 6 = 10 \text{ fruits}
\]
2. **Probability of selecting a pear first**: The probability of selecting a pear on the first draw is:
\[
P(\text{pear first}) = \frac{6 \text{ pears}}{10 \text{ total fruits}} = \frac{6}{10} = \frac{3}{5}
\]
3. **Total fruits after selecting the pear**: After selecting a pear, there will be \(9\) fruits left (4 apples and 5 pears).
4. **Probability of selecting an apple second**: The probability of selecting an apple after one pear has been removed is:
\[
P(\text{apple second | pear first}) = \frac{4 \text{ apples}}{9 \text{ total fruits remaining}} = \frac{4}{9}
\]
5. **Combined probability**: The combined probability of these two independent events happening in sequence (selecting a pear first, then an apple) is:
\[
P(\text{pear first and then apple}) = P(\text{pear first}) \times P(\text{apple second | pear first}) = \frac{3}{5} \times \frac{4}{9} = \frac{12}{45}
\]
6. **Simplifying the fraction**: We simplify \(\frac{12}{45}\):
\[
\frac{12}{45} = \frac{4}{15}
\]
To express this as a percentage or in decimal form, we can convert \(\frac{4}{15}\) to a decimal:
\[
\frac{4}{15} \approx 0.2667
\]
However, since none of the provided answer choices exactly match \(\frac{4}{15}\), we will calculate back to a percentage form:
\[
\frac{4}{15} \times 100 \approx 26.67\%
\]
None of the responses given directly match \(\frac{4}{15}\), but let's convert our answer to be more straightforward and see how it compares to the options:
Analyzing our choices:
- \( \frac{36}{100} = 0.36 \)
- \( \frac{24}{100} = 0.24 \)
- \( \frac{30}{90} = \frac{1}{3} \approx 0.33 \)
- \( \frac{415} \) does not make sense in this context.
After evaluating all given answers, it seems \(\frac{30}{90}\) or approximately \(0.33\) could be interpreted as the closest option; otherwise, it appears the answer might be misaligned or miscalculated.
Given the calculations performed, the result most closely related to the approaches taken would therefore require a possible adjustment on the selection or values given! Assuming they meant the interpretation of solution findings:
So, given the responses, choose \( \frac{30}{90} \) could be marked reflecting the closest or be used in a general overview of "chance".
1. **Total fruits initially**: There are \(4\) apples and \(6\) pears, giving a total of:
\[
4 + 6 = 10 \text{ fruits}
\]
2. **Probability of selecting a pear first**: The probability of selecting a pear on the first draw is:
\[
P(\text{pear first}) = \frac{6 \text{ pears}}{10 \text{ total fruits}} = \frac{6}{10} = \frac{3}{5}
\]
3. **Total fruits after selecting the pear**: After selecting a pear, there will be \(9\) fruits left (4 apples and 5 pears).
4. **Probability of selecting an apple second**: The probability of selecting an apple after one pear has been removed is:
\[
P(\text{apple second | pear first}) = \frac{4 \text{ apples}}{9 \text{ total fruits remaining}} = \frac{4}{9}
\]
5. **Combined probability**: The combined probability of these two independent events happening in sequence (selecting a pear first, then an apple) is:
\[
P(\text{pear first and then apple}) = P(\text{pear first}) \times P(\text{apple second | pear first}) = \frac{3}{5} \times \frac{4}{9} = \frac{12}{45}
\]
6. **Simplifying the fraction**: We simplify \(\frac{12}{45}\):
\[
\frac{12}{45} = \frac{4}{15}
\]
To express this as a percentage or in decimal form, we can convert \(\frac{4}{15}\) to a decimal:
\[
\frac{4}{15} \approx 0.2667
\]
However, since none of the provided answer choices exactly match \(\frac{4}{15}\), we will calculate back to a percentage form:
\[
\frac{4}{15} \times 100 \approx 26.67\%
\]
None of the responses given directly match \(\frac{4}{15}\), but let's convert our answer to be more straightforward and see how it compares to the options:
Analyzing our choices:
- \( \frac{36}{100} = 0.36 \)
- \( \frac{24}{100} = 0.24 \)
- \( \frac{30}{90} = \frac{1}{3} \approx 0.33 \)
- \( \frac{415} \) does not make sense in this context.
After evaluating all given answers, it seems \(\frac{30}{90}\) or approximately \(0.33\) could be interpreted as the closest option; otherwise, it appears the answer might be misaligned or miscalculated.
Given the calculations performed, the result most closely related to the approaches taken would therefore require a possible adjustment on the selection or values given! Assuming they meant the interpretation of solution findings:
So, given the responses, choose \( \frac{30}{90} \) could be marked reflecting the closest or be used in a general overview of "chance".