Alarge bag of marbles contains equal amounts of each of 10 colors. milo selects 1 marble, looks at it, puts it back, and then selects another. find the probability of milo selecting the same color both times a) 0.2 b) 0.01 c) 0.5 d) 0.1

What do we know here? We know that we have ten colors of marbles, and some number of marbles of each color. Crucially, we know that *the number of marbles of each color is equal*. Let’s call the number of marbles of each color m. Altogether, we have 10 groups of m marbles, or 10m marbles.

With that in mind, the probability of picking one particular color from all of the marbles is m/10m, or simply 1/10. Milo replaces each marble after taking it out, so we’re drawing from the same pool of marbles each time, so the probability of picking a particular color is going to be the same on the second pick as it was on the first. The chance that *both* marbles are a particular color is

(probability of picking the color on the first pick) x (probability of picking it on the second)

Or in this case:

1/10 x 1/10 = 1/100 = 0.01