Question

Explain the difference between dependent and independent events and how to find the probability with both. Give an example of each fully explaining the example and why you would solve it that way. Demonstrate to me your full understanding of what the two events mean and how to solve and work each with complete examples. Thanks a bunch!<3

Answer 1

The easiest way to discuss probability is via dice and tickets.
Dependent events require the actions preceding them to be taken into consideration.

-----Dependent Probability----
If you're pulling tickets from a hat without putting them back, each time you pull a ticket, the probability of finding a specific type changes. Let's say 100 tickets are blue and red evenly, so 50 blue, 50 red. The first ticket you pull is a 50/50 chance, or 50/100 regardless of the color. So we pull a blue ticket out. There are now 99 tickets left, 49 blue, and 50 red.
Try pulling a blue ticket now. The chances are 49/99. So the chances actually change while you pull more tickets.

-----Independent Probability----
Dice, on the other hand, don't hold any bearing on what you rolled beforehand. They're independent. Roll a die, you have a 1/6 chance per side. Roll it 30 times, each roll will still have a 1/6 chance of landing face up. No matter how many times you roll it, that chance will remain the same.

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I hope this explanation helps!