There is a bag filled with 5 blue and 6 red marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?

There are 6+5 marbles.

Of those, 5 are red.

The chances of drawing a red marble are 5/11

Since you replace the marble you drew, the chances each draw remain 5/11

You cannot draw two red marbles without drawing a red marble on your first draw, so the odds of you making a second draw are 5/11. The odds of that also being red are 5/11… but we only care about that 5/11ths the time

5/11*5/11=25/121

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