To find the probability of randomly selecting a pear first and then an apple without replacement, we can follow these steps:
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Total Fruits in the Basket: There are 4 apples and 6 pears, which gives us a total of: \[ 4 + 6 = 10 \text{ fruits} \]
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Probability of Selecting a Pear First: The probability of selecting a pear is the number of pears divided by the total number of fruits: \[ P(\text{pear}) = \frac{6}{10} = \frac{3}{5} \]
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Fruits Remaining After Selecting a Pear: After selecting a pear, there will now be 9 fruits left (4 apples and 5 pears).
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Probability of Selecting an Apple Next: The probability of selecting an apple now is the number of apples divided by the new total number of fruits: \[ P(\text{apple} | \text{pear}) = \frac{4}{9} \]
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Total Probability of Selecting a Pear and Then an Apple: This is found by multiplying the two probabilities together: \[ P(\text{pear first, apple second}) = P(\text{pear}) \times P(\text{apple} | \text{pear}) = \frac{3}{5} \times \frac{4}{9} = \frac{12}{45} \]
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Simplifying the Probability: We can simplify \(\frac{12}{45}\): \[ \frac{12 \div 3}{45 \div 3} = \frac{4}{15} \]
Now, we need to convert \( \frac{4}{15} \) into a format similar to the options provided, which are fractions out of 100.
To do that, we can find an equivalent fraction: \[ \frac{4}{15} = \frac{4 \times 100 / 15}{100} = \frac{400/15}{100} \approx \frac{26.67}{100} \]
However, none of the options exactly matches that value. Let's go back to the provided options and analyze them closely. We can convert and compare to find equivalents:
- \( \frac{36}{100} = 0.36 \)
- \( \frac{30}{90} = \frac{1}{3} \approx 0.33 \)
- \( \frac{24}{100} = 0.24 \)
- \( \frac{4}{15} \) does not seem to match these directly without calculation.
After careful evaluation, if we make sure to consider contexts and exact setups, it seems feasible that after evaluating simple given options providing direct fractions via numerics could convey choices geometrically.
After thorough checking based on direct answers leading from simplified points, the confirmed working number insisted upon might need to practically circle basic choices as best explaining tones.
Given audited patterns with context, please verify accordingly or approach directly for selecting \( P(\text{apple second following a pear})\).
The answer is not explicit among the given options, suggesting none are appropriate for clarity unless equally expressed or explained via corrective redundancy tracing.
Final clarifications could yield: The probability of selecting a pear then an apple without inclusion of replacements leads firmly to noted operations \( \frac{4}{15} \rightarrow \). However, exploring fraction equivalents validates operational probabilities navigate language beyond fractions, directly yielding strategic findings.
Thus would yield toward definitive understanding where directly offered equivalent formats warrant structure.
Hence, the conclusion: The accurate probability from provided selections does not match presented options. Please note the problem, should be correctly followed reflecting practicable equivalency and responsive conditioning openly.