To find the probability of selecting a yellow marble followed by 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 and a total of 20 marbles.
- Probability of selecting a yellow marble: \[ P(\text{Yellow}) = \frac{4}{20} = \frac{1}{5} \]
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Calculate the probability of selecting a purple marble second, after a yellow marble has already been selected.
- After selecting one yellow marble, there are now 19 marbles left, with still 4 purple marbles remaining.
- Probability of selecting a purple marble now: \[ P(\text{Purple | Yellow}) = \frac{4}{19} \]
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Calculate the combined probability of both events happening in sequence.
- Since the events are sequential, we multiply the probabilities: \[ P(\text{Yellow then Purple}) = P(\text{Yellow}) \cdot P(\text{Purple | Yellow}) = \frac{1}{5} \cdot \frac{4}{19} = \frac{4}{95} \]
Therefore, the probability of selecting a yellow marble and then a purple marble without replacement is:
\[ \frac{4}{95} \]
The correct answer is Start Fraction 4 over 95 End Fraction.
2 answers