Probability of Selecting Blue then Green Marbles with Replacement

What is the probability of selecting a blue marble on the first try and then a green marble on the second try with replacement?

This problem involves understanding the basic principles of discrete probability with a focus on experiments involving repeated trials. Probability in such contexts often requires us to identify independent versus dependent events, and tackle them using appropriate probability rules. When considering events with replacement, it's crucial to recognize that each draw from the set is independent, maintaining constant probability for each event. This simplifies the calculation since the sample space stays unchanged after each draw. Understanding these fundamentals can help solve a wide variety of probability problems of this nature.

Furthermore, solving problems like this typically involves identifying the favorable outcomes of each event and considering how the outcomes interact over multiple trials. By scrutinizing the conditions laid out in the problem, such as replacement, one can easily determine whether the given events are independent. The probability of successive independent events occurring is derived by multiplying their individual probabilities. This foundational skill in calculating compound probabilities is broadly applicable in both theoretical and real-world scenarios, including computer science applications like algorithm performance analysis and game theory. The ability to dissect the problem into measurable, understandable parts can greatly enhance your effectiveness in tackling more complex questions later on.