Independent Events: Marbles

Drawing with replacement = independent

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Drawing with ReplacementWith Replace Multiple DrawsMulti Draw Same Color TwiceSame Color

Multiple Independent Draws

What makes this a "sequence" problem?

We want a specific order: red FIRST, then blue SECOND, then red THIRD. Any other order (like blue-red-red) does NOT count as success.

Why can we multiply the individual probabilities?

With replacement, each draw is independent. The bag always has the same 10 marbles (4 red, 3 blue, 3 green). What we drew before doesn't change what's available for the next draw.

Setup:

Bag: 4 red + 3 blue + 3 green = 10 marbles. Draw 3 times with replacement.

red: 4

blue: 3

green: 3

Total: 10 marbles

Step-by-Step Solution

P(1st is red)

P(2nd is blue)

Still 10 marbles (we replaced!)

P(3rd is red)

Still 10 marbles!

Multiply (independent events):

General Formula

For n independent draws with replacement: