To find the probability of selecting a yellow marble and then a purple marble without replacement, we can follow these steps:
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Calculate the probability of selecting a yellow marble first.
There are 4 yellow marbles out of a total of 20 marbles.\[ P(\text{Yellow}) = \frac{4}{20} = \frac{1}{5} \]
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Calculate the probability of selecting a purple marble second.
After selecting a yellow marble, there are now 19 marbles left in the jar (20 - 1 = 19). The number of purple marbles remains the same, which is still 4.\[ P(\text{Purple | Yellow}) = \frac{4}{19} \]
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Combine the probabilities.
The probability of both events occurring (selecting a yellow marble first and then a purple marble) can be found by multiplying the two probabilities together:\[ P(\text{Yellow and then Purple}) = P(\text{Yellow}) \times P(\text{Purple | Yellow}) = \frac{1}{5} \times \frac{4}{19} = \frac{4}{95} \]
Thus, the probability of selecting a yellow marble without replacement and then selecting a purple marble is
\[ \boxed{\frac{4}{95}} \]
The correct answer is A. 4/95.