Tell whether the events are independent or dependent. Explain.
selecting a compact disc from a storage case and then selecting a second disc without replacing the first.
well independent means if the result of the other event has no effect on the other
Start with for example 10 in the case
then chances of getting disk A is 1/10
However when you go for the second one, the chances of getting a particular disk are 1/9
so the second trial depends on the first one.
To determine whether the events of selecting a compact disc from a storage case and then selecting a second disc without replacing the first are independent or dependent, we need to consider the impact of the first event on the second event.
In this case, the events are dependent. The reason is that the selection of the first disc affects the number of available discs for the second selection. When a disc is selected and not replaced back into the case, there is now one less disc available for the second selection. Therefore, the probability of selecting a specific disc for the second event changes based on the outcome of the first event.
To understand this, consider an example: if there are 10 discs in the storage case initially, the probability of selecting a specific disc for the first event is 1/10. After the first disc is selected, there are now only 9 discs remaining in the case. As a result, the probability of selecting the same specific disc for the second event changes to 1/9.
Therefore, the probability of the second event is dependent on the outcome of the first event, making these events dependent.