In a large bag of candy, each of the 5 colors (red, orange, yellow, blue, and green) occurs with the same probability. You reach in and select 2 candies. Find the probability that both candies are orange.

Question

In a large bag of candy, each of the 5 colors (red, orange, yellow, blue, and green) occurs with the same probability. You reach in and select 2 candies.  Find the probability that both candies are orange.

anonymous · Answer

So if there are five colors with an equal occurance than the probability of getting orange is 1/5, now given two trials and you want the result, you would multiply the probabilities. This makes sense because it should get more "difficult/improbable" as we want successive trials of the same color. Think, if you wanted a million orange in a row, that should have a tiny probability.
SO...
$$P(orange twice) = P(orange)^{2}= (\frac{1}{5})^{2}= \frac{1}{25}$$