To calculate the probability of selecting a blue marble first and then selecting a yellow marble from a jar without replacement, we can follow these steps:
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Calculate the probability of selecting a blue marble:
- There are 3 blue marbles out of a total of 16 marbles. \[ P(\text{Blue}) = \frac{3}{16} \]
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After selecting a blue marble, calculate the number of marbles left:
- After removing one blue marble, there are now 15 marbles left in total (16 - 1 = 15).
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Calculate the probability of selecting a yellow marble next:
- There are still 8 yellow marbles remaining out of the 15 remaining marbles. \[ P(\text{Yellow | Blue}) = \frac{8}{15} \]
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Multiply the probabilities of the two events together: \[ P(\text{Blue and then Yellow}) = P(\text{Blue}) \times P(\text{Yellow | Blue}) \] \[ P(\text{Blue and then Yellow}) = \frac{3}{16} \times \frac{8}{15} \] \[ = \frac{3 \times 8}{16 \times 15} \] \[ = \frac{24}{240} \] \[ = \frac{1}{10} \]
Thus, the probability of selecting a blue marble and then selecting a yellow marble is \( \frac{1}{10} \).
So the correct answer is: \[ \boxed{\frac{1}{10}} \]