To find the probability of selecting a blue marble followed by a yellow marble (without replacement), we can use the formula for conditional probability.
-
Determine the total number of marbles. There are 16 marbles in total (5 red + 3 blue + 8 yellow).
-
Calculate the probability of selecting a blue marble: The probability of picking a blue marble first is: \[ P(\text{Blue}) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{3}{16} \]
-
Calculate the probability of selecting a yellow marble after removing one blue marble: After one blue marble is removed, there are 15 marbles left in total, and the number of yellow marbles remains at 8. Thus, the probability of picking a yellow marble next is: \[ P(\text{Yellow} | \text{Blue}) = \frac{\text{Number of yellow marbles}}{\text{Total marbles left}} = \frac{8}{15} \]
-
Find the combined probability of both events: The combined probability of both selecting a blue marble and then a yellow marble is found by multiplying the two probabilities: \[ P(\text{Blue and then Yellow}) = P(\text{Blue}) \times P(\text{Yellow} | \text{Blue}) = \frac{3}{16} \times \frac{8}{15} \]
-
Calculating the combined probability: \[ P(\text{Blue and then Yellow}) = \frac{3 \times 8}{16 \times 15} = \frac{24}{240} = \frac{1}{10} \]
Therefore, the probability of selecting a blue marble and then selecting a yellow marble is: \[ \frac{1}{10} \]
So the answer is: Start Fraction 1 over 10 End Fraction