Question

A large 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

Answer 1

b. 0.01

hope this helps

Answer 2

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