Video Transcript
A box contains 10 red marbles, three white marbles, and 17 blue marbles. If a marble is picked from the box at random, what is the probability that the marble is not blue?
We begin by recalling that the probability of an event is the chance or likelihood it happens. In this question, we are asked to find the probability that a selected marble is not blue. We are told that there are 10 red, three white, and 17 blue marbles in a box. This means that there are 30 marbles in total. The probability of selecting a blue marble, which we will write 𝑃 of 𝐵, is therefore equal to 17 out of 30, as 17 out of the 30 marbles are blue.
We recall that probabilities sum to one and that the complement of an event is written 𝐴 bar or 𝐴 prime such that the probability of 𝐴 bar is equal to one minus the probability of 𝐴. The probability of not selecting a blue ball is therefore equal to one minus 17 over 30. This is the same as 30 over 30 minus 17 over 30. And subtracting the numerators gives us 13 out of 30. This is the probability of selecting a marble that is not blue.
An alternative method here would be to find the sum of the other colored marbles. There are 10 red and three white marbles in the box, and 10 plus three is equal to 13. This confirms that the probability of selecting a marble that is not blue is 13 out of 30.
