Final answer:
The probability of picking a yellow marble and then a blue marble from the box is the product of the individual probabilities of each event: (1/6) × (1/5), which equals 1/30 or approximately 3.33%.
Step-by-step explanation:
The student has asked about the probability of selecting a yellow marble and then a blue marble from a box containing different colored marbles. To solve this, we follow a two-step process, as the second event depends on the outcome of the first event (since the first marble is not replaced).
First, we find the probability of picking a yellow marble. Since there is 1 yellow marble out of a total of 6, the probability is ⅖1/6 or about 16.67%.
After picking the yellow marble, there are now 5 marbles left in the box (3 red, 1 blue, and 1 green). The probability of then picking a blue marble from these remaining marbles is 1/5, as there is one blue marble out of five.
To find the overall probability of both events happening in sequence (picking a yellow marble and then a blue marble), we multiply the probabilities of the individual events: (1/6) × (1/5), which equals 1/30 or approximately 3.33%.