Video: Determining the Probability of the Intersection of Two Events

A bag contains 41 balls. There are 28 red balls which are numbered 1 to 28 and 13 white balls which are numbered 29 to 41. If a ball is chosen from the bag at random, what is the probability of the ball being red and having an even number?

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Video Transcript

A bag contains 41 balls. There are 28 red balls which are numbered one to 28 and 13 white balls which are numbered 29 to 41. If a ball is chosen from the bag at random, what is the probability of the ball being red and having an even number?

The equation we will use in order to work out this probability is as follows: probability is equal to the number of successful outcomes divided by the number of possible outcomes. In order to find the probability here, we need to find the number of successful outcomes in this problem and the number of possible outcomes in this problem.

We will start by looking at the possible outcomes in this problem. The bag contains 41 balls. There are 28 red balls which are numbered one to 28 and 13 white balls numbered 29 to 41. So in total, there are 41 balls. And this means if a ball is chosen from the bag at random that there are 41 possible different outcomes.

Next, we need to find how many successful outcomes there are. Now, for an outcome to be successful, the ball that is selected from the bag has to be red and it has to have an even number on it. So we need to find how many out of the 41 balls are red and have an even number. We know that there are 28 red balls. However, not all of them have even numbers on. So the balls numbered one to 28 are all red.

Now, we just need to find how many numbers between one and 28 are even. So let’s write out all the numbers that are even between one and 28. So we have two, four, six, eight, 10, 12, 14, 16, 18, 20, 22, 24, 26, and 28. And so in total, there are 14 even numbers between two and 28. And so this means there are 14 red balls which have an even number on them. And so therefore, there are 14 possible successful outcomes.

Finally, all we need to do is put the number of successful outcomes and the number of possible outcomes into our equation for the probability. And this gives us that the probability of a randomly chosen ball from the bag being red and having an even number is 14 over 41.

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