Question

sample response: the events are dependent, so the sample space changes for the second draw. after drawing the first marble, there are only 11 marbles left. the probability is (\frac{2}{12})(\frac{4}{11}) = \frac{8}{132}, or \frac{2}{33}. check all that you included in your response. these are dependent events. the sample space is reduced from 12 to 11 for the second draw. to find the probability, multiply the probability of choosing yellow by the probability of choosing red after yellow.

Explanation:

Step1: Identify event - dependence

The first draw affects the second, so they are dependent events.

Step2: Analyze sample - space change

Initial sample space is 12 marbles. After first draw, it becomes 11 marbles.

Step3: Calculate probability

If probability of first (yellow) is $\frac{2}{12}$ and second (red) after yellow is $\frac{4}{11}$, then overall probability is $\frac{2}{12}\times\frac{4}{11}=\frac{8}{132}=\frac{2}{33}$.

Answer:

All of the following should be included:

• These are dependent events.
• The sample space is reduced from 12 to 11 for the second draw.
• To find the probability, multiply the probability of choosing yellow by the probability of choosing red after yellow.