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Video: Finding the Theoretical Probability in Word Problems Involving Marbles

Kathryn Kingham

A box contains 7 white balls, 3 black balls, and 8 red balls. What is the probability that a ball drawn at random is black?


Video Transcript

A box contains seven white balls, three black balls, and eight red balls. What is the probability that a ball drawn at random is black? The probability of an event is equal to the number of favorable outcomes over the number of possible outcomes.

We will need to answers some questions. The first question is what event are we specifically looking at. The next one is what would be the favorable outcome and how many times could that happen? And third, what is all the possible outcomes of this random action?

Starting with the event, what event are we looking at? We want to look at the case that a black ball is drawn. And then we want to know how many times would that be possible out of our set. Out of our set, there’re three black balls. The number of favorable outcomes in this case would be three. And the total number of possible outcomes for us, well we have 18 total balls in the box, which means we have 18 possible outcomes. Three out of 18, that’s our probability.

But in some cases, we might want to simplify this probability. Here we see that both three and 18 are divisible by three. We can call our theoretical probability one-sixths. This is the probability that we calculated written in its simplest form. The probability that a black ball is drawn at random is one-sixths.