## morningskye123 one year ago Part 1: Using your own words, describe two events that are independent. Use math vocabulary that you have learned so far in this module to explain what it means when events are independent. I really hate these type of question. @mathstudent55 can you help?

1. mathstudent55

How can I possibly know the vocabulary you have learned when I have no access to your learning materials?

2. morningskye123

Lol, sorry. I just assume because probability is more about looking at a chart. But can you explain to me what an independent event is?

3. mathstudent55

Ok. Now at least you're learning probability. Independent events are events in which the outcome of one event is not affected by the outcome of another event. Here is an example. You have a bag with 4 marbles, one each: white, blue, red and green.

4. mathstudent55

You are going to draw two marbles. What is the probability that you will draw the green one followed by the blue one?

5. morningskye123

won't is be a 25% chance?

6. mathstudent55

If after you draw one marble, you do not replace it, and then you draw the second marble, then the two drawings are not independent because the drawing of the first marble will affect the outcome of the second drawing.

7. mathstudent55

If, on the other hand, after you draw the first marble, you replace it in the bag, then you do the second drawing, then the second drawing is exactly like the first drawing, and the outcome of the first drawing does not affect the outcome of the second drawing. When there is replacement, the events are independent.

8. morningskye123

So by replacing what you take, will not effect the outcome making it independent

9. mathstudent55

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10. mathstudent55

You are correct.

11. mathstudent55

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12. morningskye123

yaay lol

13. mathstudent55

As you can see, only one outcome of each type is the desired outcome of green followed by blue. Since the number of total outcomes is different, then the probabilities are different depending on whether there is replacement or not. Without replacement, p = 1/12 With replacement, p = 1/16 Remember that "with replacement" means the two drawings are independent events.

14. morningskye123

Oooh mind blown. Thanks I understand

15. mathstudent55

You are welcome. BTW, the way I calculated the probabilities is not a practical way. I used it to illustrate the difference between dependent and independent events. By seeing all the outcomes, and also the only desired outcome, it's easy to calculate the probabilities. Of course, there is a much better way of calculating these probabilities without having to list all the possible outcomes.

16. mathstudent55

You are welcome.