Video: Determining the Theoretical Probability of an Event in a Marbles Problem

A bag contains 7 white marbles, 8 black marbles and 7 red marbles. If a marble is chosen at random from the bag, what is the probability that it is white?

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Video Transcript

A bag contains seven white marbles, eight black marbles, and seven red marbles. If a marble is chosen at random from the bag, what is the probability that it is white?

So if we’re looking to find the probability that our marble is white, what we’re gonna use is actually we can use this equation here that says the probability of an event happening is equal to the number of events present divided by the total number of outcomes.

So in our question, what that means is 𝑃 white, which means the probability that it’s going to be white, is equal to — well it then says the number of events.

What that actually means is the number of actual white marbles in the bag cause white marbles are the event that we’re looking for in this question.

So in this case, looking at the question, it says that there are seven white marbles. And then this is gonna be over the total number of outcomes.

And our question, total number of outcomes means total number of marbles, which is gonna be seven, because it’s seven white marbles, plus eight, cause it’s eight black marbles, plus seven, cause that’s seven red marbles.

Okay, great! Okay, so we actually get as our denominator 22, because it’s seven plus eight which is 15 plus seven which is 22. So therefore, we can say that if a marble is chosen at random from the bag, the probability of it being white is equal to seven over 22.

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