Question Video: Identifying Certain Events Mathematics

If there are three red balls and nothing else in a bag, is it certain, possible, or impossible that if I pick out a ball at random it will be red?

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Video Transcript

If there are three red balls and nothing else in a bag, is it certain, possible, or impossible that if I pick out a ball at random, it will be red?

This is quite a wordy question really. So let’s go through it really slowly to understand what it’s asking. Firstly, we’ve got a description and that’s of three red balls and nothing else in a bag. Let’s sketch them. Here are our three balls. And let’s use this circle to represent the bag that they’re in. Now, there’s a really important part of that first phrase that we haven’t mentioned yet. And, it’s these two words here. We’re told that there are three red balls and nothing else in the bag. There aren’t any other colors. There aren’t any other objects. Those three red balls are the only things in that bag.

Now this question is all about what’s gonna happen if we pick out a ball at random. When something like this happens at random, it happens by chance, without any planning or decision-making. If we wanted to pick a ball at random, maybe we’d close our eyes or, like in the example of this question, we put the balls inside a bag where we can’t see them. This way, we can’t choose what we pick. Now the color that we’re asked about is red.

So this question is asking us, what’s the chance that we’re going to pick a red ball? And we’re given three possible answers. Is it certain that we pick a red ball? Is it possible that we pick a red ball? Or is it completely impossible that we pick a red ball? We know that the word ”impossible” means there’s no chance at all. It’s definitely not going to happen. Now, if we put our hand into that bag, we can’t say there’s no chance at all of us pulling out a red ball. We could say it’s impossible we’d pick out a green ball. It’s impossible we’re going to pull out a cheeseburger. But we can’t say it’s impossible we’re going to pull out a red ball. The bag’s full of them.

Let’s get rid of this as a possible answer. Speaking of possible, is it possible that we pull out a red ball? We know that when something is possible, there is a chance of it happening. It might happen; it could happen. Now this word sounds like it could be right. It is possible that we pull out a red ball. But it’s time to come back to those two words in that first phrase that we said were so important. There are three red balls and nothing else in a bag. We wouldn’t use the word possible to describe the chance of us pulling out a red ball. It’s much more than that. It’s absolutely certain because there’s nothing else in that bag.

If we put our hand in, wiggle it around, and pull out a ball, it’s going to be red, definitely. And if something is definitely going to happen, we use the word ”certain.” If you’re not sure about this, try it. If you don’t have colored balls, then try three coins that are the same. As long as you don’t put anything else in your bag, then you’ll see that the chance of you pulling out a red ball or one of your coins is certain. If there are three red balls and nothing else in a bag, the chance of us randomly picking out a ball and it being red is certain.