To find the probability of selecting a blue marble and then a yellow marble without replacement, we can break this down into two steps:
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Calculating the probability of selecting a blue marble: There are a total of 16 marbles (5 red + 3 blue + 8 yellow). The probability of selecting a blue marble is: \[ P(\text{Blue}) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{3}{16} \]
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Calculating the probability of selecting a yellow marble after a blue marble has been taken out: After removing a blue marble, the total number of marbles left in the jar is 15 (16 - 1 = 15). Now, the number of yellow marbles remains 8. The probability of selecting a yellow marble after selecting a blue marble is: \[ P(\text{Yellow | Blue}) = \frac{\text{Number of yellow marbles}}{\text{Total number of marbles left}} = \frac{8}{15} \]
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Calculating the combined probability: The combined probability of both events happening (selecting a blue marble, then a yellow marble) is found by multiplying the two probabilities: \[ P(\text{Blue and then Yellow}) = P(\text{Blue}) \times P(\text{Yellow | Blue}) = \frac{3}{16} \times \frac{8}{15} \] To compute this, we can multiply the fractions: \[ P(\text{Blue and then Yellow}) = \frac{3 \times 8}{16 \times 15} = \frac{24}{240} \]
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Simplifying the probability: Simplifying \(\frac{24}{240}\) gives: \[ \frac{24 \div 24}{240 \div 24} = \frac{1}{10} \]
Thus, the probability of selecting a blue marble and then selecting a yellow marble is \(\frac{1}{10}\).
The correct answer is C. 1/10.