Probability  Independent Events Example  Don't Memorise  Summary and Q&A
TL;DR
Understanding the concept of independent and dependent events in probability when drawing marbles from a box.
Key Insights
 🍱 Drawing marbles from a box can be used as an example to understand the concept of independent and dependent events in probability.
 💱 The probability of an event in the first draw may or may not change for the second draw, depending on whether the marbles are replaced.
 ⚾ Independent events are those in which the probability remains the same even after the occurrence of the first event, while dependent events are those in which the probability changes based on the outcome of the first event.
 👾 The sample space, which refers to the total number of possible outcomes, plays a crucial role in determining the independence or dependence of events.
 The understanding of independent and dependent events helps in accurately calculating probabilities and making predictions in various reallife situations.
 ❓ Replacing or not replacing the marbles after each draw affects the probability of subsequent draws.
 ❓ The concept of independent and dependent events extends beyond marbles and can be applied to various other scenarios involving probability calculations.
Transcript
Let's understand another example on a new page. Assume you have three red marbles and three blue marbles in a box. Your task is to pull out two marbles out of these six marbles, one after the other. This example is interesting, but I need you to focus really really hard. So there will be two cases here! First case, you pick the first marble out and... Read More
Questions & Answers
Q: What is the probability of drawing a red marble in the first chance when the marble is replaced?
The probability is three out of six, as there are three red marbles and six marbles in total. The event is independent because the marbles are replaced, and the sample space remains the same.
Q: What happens to the probability if the marbles are not replaced after the first draw?
The probability changes. In this case, if a red marble is drawn in the first chance, the probability of drawing another red marble decreases to two out of five. The events are dependent because the sample space changes, and the outcome of the first draw affects the second draw.
Q: How does replacing or not replacing the marbles affect the probability of drawing a red marble?
If the marbles are replaced, the probability remains the same for each draw. If the marbles are not replaced, the probability may change as the sample space changes, and the outcome of the first draw affects the probability of the second draw.
Q: What is the significance of understanding independent and dependent events in probability?
Understanding independent and dependent events is crucial in probability as it helps determine the likelihood of outcomes in various scenarios. It allows us to calculate probabilities accurately and make informed decisions based on the nature of the events.
Summary & Key Takeaways

If the marbles are replaced after each draw, the probability of picking a red marble remains the same for both the first and second draw.

If the marbles are not replaced, the probability of picking a red marble changes for the second draw.

The independence or dependence of events in probability depends on whether the sample space changes after each draw.