To find the probability of selecting a yellow marble first and then a purple marble without replacing the first marble, we can follow these steps:
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Determine the total number of marbles and the number of yellow marbles.
- Total marbles: 20
- Yellow marbles: 4
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Calculate the probability of selecting a yellow marble first. \[ P(\text{yellow}) = \frac{\text{Number of yellow marbles}}{\text{Total number of marbles}} = \frac{4}{20} = \frac{1}{5} \]
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Now, determine the total number of marbles remaining after removing one yellow marble.
- After selecting one yellow marble, the remaining total is \(20 - 1 = 19\) marbles.
- The number of purple marbles is still \(4\).
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Calculate the probability of selecting a purple marble next. \[ P(\text{purple | yellow selected}) = \frac{\text{Number of purple marbles}}{\text{Total number of remaining marbles}} = \frac{4}{19} \]
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Now multiply the probabilities to find the combined probability of both events occurring. \[ P(\text{yellow and then purple}) = P(\text{yellow}) \times P(\text{purple | yellow selected}) = \frac{1}{5} \times \frac{4}{19} \]
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Performing the multiplication: \[ P(\text{yellow and then purple}) = \frac{1 \times 4}{5 \times 19} = \frac{4}{95} \]
Therefore, the probability of selecting a yellow marble first and then a purple marble without replacement is:
\[ \frac{4}{95} \]
So, the correct answer is: Start Fraction 4 over 95 End Fraction.