Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A bag holds red, blue and green marbles. Two marbles are taken, one after the other. Find the probability that both are blue (a) if the first marble is put back, (b) if it is not put back.
List all the equally likely pairs and count. For events that do not affect each other, multiply. For at least one, take the chance of none from 1. Without putting back, the second chance changes.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Put back. .
Step 2. Not put back. .
Step 3. Why smaller. Once a blue marble is out, a second blue one is less likely.
Answer: and .
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