Wendy picks a marble at random, puts it back, and then picks another marble at random.Are these two events dependent or independent?dependentindependent

Accepted Solution

Independent. Two events are dependent if knowing the result of the first one influences what you'd expect from the second.Consider this example: if I have a sack with 3 black marble and 1 white marble, I have probability 75% of picking a blakc marble, and 25% of picking the white one.If I pick the white one, and don't replace, the second pick will be dependent on the first one, because now I'm sure that I'll pick one of the black marbles, since they are the only ones left in the sack.In your example, though, Wendy replaces the marble she picks first. This means that the second pick will take place in the exact same conditions of the first one, and knowing which marble she picked at first doesn't affect in any way the result of the second pick.As another example, consider rolling two dice. Suppose that the first die lands showing 4. Does this affect in any way what you'd expect from the second die? Well, no: the numbers 1-6 are still equally probable to show up.