A box contains 5 red, 2 white, & 3 blue marbles. If a marble is selected at random, what is the probability that it is not red?
We have a box with 10 marbles: 5 Red, 2 White, 3 Blue.
The probability of picking any one marble at random is
We're asked for the probability that the marble we pick at random isn't red. So let's do this in two ways:
Direct calculation of non-red marbles
There are 5 marbles that are not red: 2 white and 3 blue. There are, therefore, 5 marbles out of the 10 that aren't red, so the probability of picking either a white or blue marble (and therefore not a red one) is:
Indirect calculation of non-red marbles
We can see that there are 5 red marbles out of the total marble count of 10. Therefore, we can deduct the chance of getting a red marble from the sum of all choices (100%) and calculate the chance of getting a non-red marble: