To find the probability of selecting a yellow marble first and then a purple marble without replacement, we can break it down into two steps:
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Probability of selecting a yellow marble: 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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Probability of selecting a purple marble after selecting a yellow marble: After selecting a yellow marble, there will be 19 marbles left in total (since we are not replacing the yellow marble), and still 4 purple marbles. \[ P(\text{Purple} | \text{Yellow}) = \frac{4}{19} \]
Now, to find the combined probability of these two events happening in sequence, we multiply the probabilities: \[ P(\text{Yellow and then Purple}) = P(\text{Yellow}) \times P(\text{Purple} | \text{Yellow}) = \frac{1}{5} \times \frac{4}{19} = \frac{4}{95} \]
Thus, the probability of selecting a yellow marble first and then a purple marble is
\[ \frac{4}{95} \]
The correct answer is Start Fraction 4 over 95 End Fraction.
2 answers