Numbered disks are placed in a box and one disk is selected at random. There are 6 red disks numbered 1 through 6, and 7 yellow disks numbered 7 through 13. In an experiment a disk is selected, the number and color noted, replaced, and then a second disk is selected. Is this an example of independence?
I would say so.
Yes, once the first disk is replaced, the event B (the selection of the second disk) does not depend on the first one.
In order to determine if this experiment is an example of independence, we need to examine whether the outcome of selecting the first disk affects the outcome of selecting the second disk.
In this experiment, the disk is replaced after noting its number and color. This means that the probability distribution of disks remains constant throughout the experiment.
Since the probabilities for selecting a certain color or number of disk remain the same for the second selection, despite the outcome of the first selection, we can conclude that this experiment is an example of independence. The outcome of selecting the first disk does not affect the outcome of selecting the second disk.
To determine whether this experiment is an example of independence, we need to understand what independence means in the context of probability.
Two events are considered independent if the occurrence of one event does not affect the probability of the other event. In other words, if the probability of one event happening remains the same regardless of whether the other event has occurred.
In this case, let's consider the two events:
Event A: Selecting a disk and noting its number and color.
Event B: Selecting a second disk.
To determine if these events are independent, we need to check if the probability of Event A remains the same regardless of the occurrence of Event B, and vice versa.
In the given experiment, a disk is selected, and then another disk is selected. The fact that the disks are replaced after each selection means that the probability of selecting each disk remains constant throughout the experiment.
Since the probability of selecting a disk is not affected by the previous selection (i.e., the number and color of the first disk), we can conclude that this experiment is an example of independence.
In summary, the experiment of selecting numbered disks is an example of independence since the occurrence of selecting a disk and noting its number and color does not affect the probability of selecting a second disk.