Two-way table: boys 12 cat 8 dog, girls 10 cat 20 dog; P(dog) Easy

The question

Question: A survey asked boys and girls: cat or dog?

Boys: 12 cat, 8 dog.

Girls: 10 cat, 20 dog.

One person is picked at random.

Find P(dog).

1 Make the table

One row for each group, one column for each answer, and a total for each.

The four counts go inside.

Row totals: 12 plus 8 is 20.

10 plus 20 is 30.

Column totals: 22 and 28.

And 50 people in all.

The totals sit at the edges, in the margins.

2 A total over all

All the dog: 28.

Everyone: 50.

So P of dog is 28/50.

Careful!

The bottom is everyone, 50.

Not only the other 22.

Both 28 and 50 can be divided by 2.

That makes it simpler.

So it is 14/25.

3 Check

Let's check.

The four cells add up to 50, everyone.

The table is right.

And the two cells of dog add up to its total: 8 plus 20 is 28.

So the answer is right!

Let's look back.

First: make the table.

Then: a total over all.

Last: check.

▶ Watch it solved

Two-way table: boys 12 cat 8 dog, girls 10 cat 20 dog; P(girl and… Medium

The question

Question: A survey asked boys and girls: cat or dog?

Boys: 12 cat, 8 dog.

Girls: 10 cat, 20 dog.

One person is picked at random.

Find P(girl and dog) and P(dog given girl).

1 Make the table

One row for each group, one column for each answer, and a total for each.

The four counts go inside.

Row totals: 12 plus 8 is 20.

10 plus 20 is 30.

Column totals: 22 and 28.

And 50 people in all.

The totals sit at the edges, in the margins.

2 One cell over all

Girl and dog: both at once.

That is one cell, 20.

Out of everyone, 50.

So P of girl and dog is 20/50.

Careful!

And means out of everyone: 50.

Over 28 would be given dog.

Both 20 and 50 can be divided by 10.

So it is 2/5.

3 Keep only the given row

Given girl: only this row counts.

In it: 20 dog, out of 30.

So P of dog given girl is 20/30.

Both 20 and 30 can be divided by 10.

So it is 2/3.

So: P of girl and dog is 2/5.

P of dog given girl is 2/3.

4 Check

Let's check.

The four cells add up to 50, everyone.

The table is right.

And the and rule: P of girl, 30/50, times P of dog given girl, 20/30.

The 30s cancel: 20/50.

So the answer is right!

Let's look back.

First: make the table.

Then: one cell over all.

Then: keep only the given row.

Last: check.

▶ Watch it solved

Two-way table: men 16 yes 4 no, women 12 yes 8 no; P(yes), P(woman… Harder

The question

Question: A survey asked men and women: yes or no?

Men: 16 yes, 4 no.

Women: 12 yes, 8 no.

One person is picked at random.

Find P(yes), P(woman and no) and P(no given woman).

1 Make the table

One row for each group, one column for each answer, and a total for each.

The four counts go inside.

Row totals: 16 plus 4 is 20.

12 plus 8 is 20.

Column totals: 28 and 12.

And 40 people in all.

The totals sit at the edges, in the margins.

2 A total over all

All the yes: 28.

Everyone: 40.

So P of yes is 28/40.

Careful!

The bottom is everyone, 40.

Not only the other 12.

Both 28 and 40 can be divided by 4.

So it is 7/10.

3 One cell over all

Woman and no: both at once.

That is one cell, 8.

Out of everyone, 40.

So P of woman and no is 8/40.

Both 8 and 40 can be divided by 8.

So it is 1/5.

4 Keep only the given row

Given woman: only this row counts.

In it: 8 no, out of 20.

So P of no given woman is 8/20.

Both 8 and 20 can be divided by 4.

So it is 2/5.

So: P of yes is 7/10.

P of woman and no is 1/5.

P of no given woman is 2/5.

5 Check

Let's check.

The four cells add up to 40, everyone.

The table is right.

And the two cells of yes add up to its total: 16 plus 12 is 28.

So the answer is right!

Let's look back.

First: make the table.

Then: a total over all.

Then: one cell over all.

Then: keep only the given row.

Last: check.

▶ Watch it solved