An example of dependent events is selecting a purple tulip from the first vase and then selecting a ____________.
a yellow tulip from the same vase, after replacing the first tulip.
Explanation:
When we talk about dependent events in probability, we are referring to events where the outcome of one event affects the probability of the next event. In this scenario, the probability of selecting a yellow tulip from the same vase after selecting a purple tulip is influenced by the initial selection.
Let's break it down based on the given data. The first vase contains eight purple tulips and six yellow tulips, while the second vase contains five purple tulips and nine yellow tulips. If we select a purple tulip from the first vase, the total number of tulips left in the vase decreases, affecting the probability of selecting a yellow tulip next.
After choosing a purple tulip from the first vase, there are now only 13 tulips left in the vase, out of which 6 are yellow. This means the chances of picking a yellow tulip after a purple tulip are lower compared to selecting a yellow tulip without any previous selection.
This example showcases how the outcome of one event can impact the probability of a subsequent event, demonstrating the concept of dependent events in probability theory.
Therefore, the correct answer to the given question is selecting a yellow tulip from the same vase, after replacing the first purple tulip.