To find the probability of selecting a blue marble and then a yellow marble without replacement, we 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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Calculate the probability of selecting a yellow marble after selecting a blue marble. After selecting one blue marble, there are now 15 marbles left in total (16 - 1 = 15). The number of yellow marbles remains 8. \[ P(\text{Yellow} | \text{Blue}) = \frac{8}{15} \]
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Multiply these probabilities together to get the final probability. \[ P(\text{Blue then Yellow}) = P(\text{Blue}) \times P(\text{Yellow} | \text{Blue}) = \frac{3}{16} \times \frac{8}{15} \]
Now, performing the multiplication: \[ P(\text{Blue then Yellow}) = \frac{3 \times 8}{16 \times 15} = \frac{24}{240} \]
Now simplify \(\frac{24}{240}\): \[ \frac{24}{240} = \frac{1}{10} \]
So, the final probability of selecting a blue marble and then a yellow marble is: \[ \frac{1}{10} \]
Thus, the answer is \(\frac{1}{10}\).