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What does "with replacement" mean?
After drawing a marble and noting its color, you put it back in the bag and mix thoroughly. The bag returns to its original state before the next draw.
Why does this create independence?
After replacing, the bag looks exactly the same as before. The second draw "doesn't know" what color we got on the first draw. Both draws face the same 8 marbles (5 red + 3 blue).
The key test for independence:
Ask: "Does knowing the first result change the probability of the second?" With replacement, the answer is no — the bag is reset!
First draw
8 marbles total: 5 red, 3 blue
Replace the marble
Back to 8 marbles: 5 red, 3 blue
Second draw
Same probabilities as before!
Key Point:
Because we put the marble back, the second draw is exactly like the first. The bag is always the same!