# Lesson video

In progress...

Hi, I'm Mrs. Bennet.

And in this lesson, we're going to be finding conditional probabilities from, to-way tables.

In this question, we are given a two-way table.

It shows the information about year seven and eight students and their participation in some school clubs.

So, we've got chess, art, debate and film clubs, and then we can see which year groups the students are in.

Before we start, It will be useful to find the totals for attendance at each club and find the total number of students as we will need these for parts a and b.

So, we add an extra column and an extra roll to the table for the totals like this.

Now, for part a, we want to focus on film club.

We want to find the probability that two students picked at random attend film club.

There are 29 students out of a hundred who attend film club.

So, the probability of picking at the first student is 29 out of 100.

Once that student has been picked, there will be 28 students left in the film club and 99 students in total.

So, now the probability of picking a student who attends film club is 28 out of 99.

We multiply these probabilities together to get 812 over 9,900.

And we can simplify that to get 203 out of 2,475.

You may be wondering, why the students in year seven or year eight or whether the students are in year seven or year eight we don't know which is why I put question marks in the two-way table.

And we don't actually need to worry about this, as we are only focusing on the fact that the two students attend film club.

You don't need to put question marks in your table though.

This is just for me to illustrate that to you.

Now, let's look at part B.

This time it does matter which year that those students are in.

We want to focus on art club for year seven and year eight.

So, we might pick a year seven first.

This is 16 out of 100 as a probability.

Then we have to pick a year eight.

So, this would be 8 out of 99.

However, we could instead have chosen a year eight student first and then a year seven.

So, that would have given us 8 out of 100 multiplied by 16 out of 99 , because there are two different scenarios here, namely choosing a year seven and then a year eight, or choosing a year eight, and then year seven.

We add together these probabilities, which gives us 64 out of 2,475 when simplified.

Here are some questions for you to try.

Pause the video to complete the task and restart when you were finished.

Here are the answers.

The probability that a student likes pop is 30 over 130.

Probability of selecting a second student who likes pop is 29 over 129.

Multiply these probabilities together to get 29 over 559.

For part B.

We can select a male student who likes rock and a female student who likes rock giving us 17 out of 30, multiply by 30 over 129.

Or, we can select a female student who likes rock first and then a male student who likes rock.

So, this will be 30 over 130 multiplied by 17 over 129.

Add the probabilities together from each scenario.

And we get 34 over 559.

Here's some questions for you to try.

Pause the video, to complete the task and restart when you were finished.

Here are the answers.

It's useful to find the totals first by adding an extra row and an extra column to the table.

Then for part a, we find the probability a student has school dinners.

This is 80 out of 170.

So, student who have school dinners is 79, out of 169 multiply together to get 632, out of 2,873 For part B, we have two scenarios.

Both students have a packed lunch, or, both students have a school dinner.

So, we calculate 90 over 170 multiplied by 89, over 169 for packed lunches.

And we add the results of multiplying 80, over 170 by 79, over 169 for two students having school dinners.

This gives us 1,433 out of 2,873 as our probability.

That's all for this lesson.

Remember to take the exit quiz.

Thank you for watching.