Lesson video

Hi, I'm Mrs Denny.

And in this lesson we're going to be looking at finding probabilities from Venn diagrams, concerning three sets.

Here's a Venn diagram with three sets.

We want to firstly, work out the probability that a number is in A union B union C.

There are eight numbers in A or B or C out of ten numbers altogether in a universal set.

So the probability of A union B union C is eight out of ten which can be simplified to four fifths.

Next we're asked to find the probability A or B, A union B, there are six numbers of A or B.

So the probability is six out of ten or three fifths When simplified.

In part C we're asked for conditional probability, the probability that a number is in A and B, given that the number is in B there are three numbers of A intersect B that's in the overlap of A and B.

There are four numbers of set B so the probability of A and B given that the number is in B is three quarters, three out of four.

Finally, we want the probability that it's not in A intersect B, given that the number is in B imagine shared in the compliment of A and circle B, which sections have been shared in twice, it's the section where two is so we have one number out of four in set B so that gives us a probability of one quarter.

Here's a question to you to try pause the video to complete the task and restart when you are finished.

Here are the answers the probability for part A can be found using the overlap of all three sets There are six students here, the probability of A union G these are students who picked art or geography any sections within these circles So we work out three at six at two at eight at four, which gives us twenty three.

So the probability is twenty three out of twenty seven.

For part C, we want the overlap of art and drug effect, which is eight out of twenty.

For part D, we want the overlap of art and geography again but crucially, this time is given that they do history already.

So there are only six students who chose all three subjects out of eighteen, who do history.

So the probability of art and geography given that the student does history is six out of eighteen.

Here's a question for you to try pause the video to complete the task and restart When you are finished.

Here are the answers for part A, we want anyone who doesn't like apples and those who choose bananas.

So shared the compliment of circle A and then shared circle B and include the parts that you have shared it twice in your probability as we want that intersect to these two things.

This is eleven plus two people So thirteen out of forty seven altogether.

For part B, we can use the same sections as we shared it in part A but we have that the person is already a fan of bananas.

So we look for the total circle B, which is eighteen so our probability is thirteen out of eighteen.

For part C, we need the intersection of apples and oranges given that they already liked bananas.

So this is one person out of eighteen.

Finally, we want the probability that they'll like apples or oranges given that they like bananas.

So this is four plus one, plus two giving us seven people who like apples or oranges out of eighteen who already like bananas.

That's all for this lesson.

Remember to take the exit quiz.

Thank you for watching.