To calculate the probability of selecting a blue marble and then a yellow marble without replacement, we can follow these steps:
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Find the total number of marbles: There are 16 marbles in total (5 red + 3 blue + 8 yellow).
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Calculate the probability of selecting a blue marble first: \[ P(\text{blue}) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{3}{16} \]
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After selecting a blue marble, the total number of marbles left is 15 (since we do not replace the blue marble). The number of yellow marbles remains the same (8 yellow marbles).
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Calculate the probability of selecting a yellow marble after removing a blue marble: \[ P(\text{yellow | blue}) = \frac{\text{Number of yellow marbles}}{\text{Total number of remaining marbles}} = \frac{8}{15} \]
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Calculate the combined probability of both events (selecting a blue marble first, then a yellow marble): \[ P(\text{blue and then yellow}) = P(\text{blue}) \times P(\text{yellow | blue}) = \frac{3}{16} \times \frac{8}{15} \]
We can compute this step: \[ P(\text{blue and then yellow}) = \frac{3 \times 8}{16 \times 15} = \frac{24}{240} \] Simplifying \(\frac{24}{240}\): \[ \frac{24 \div 24}{240 \div 24} = \frac{1}{10} \]
The correct probability of selecting a blue marble and then a yellow marble without replacement is:
\[ \boxed{\frac{1}{10}} \]