Boys 12 cat 8 dog, girls 10 cat 20 dog, P(dog given girl) Easy

The question

Question: People were asked: cat or dog?

12 boys chose cat and 8 chose dog.

10 girls chose cat and 20 chose dog.

One of the girls is picked at random.

What is the probability they chose dog?

The line means given.

Given one of the girls: we only look at the girls.

P stands for probability.

The line stands for given.

1 Make a table

One row for each group, one column for each answer, and the totals.

12 boys chose cat, 8 chose dog.

12 plus 8 is 20.

10 girls chose cat, 20 chose dog.

10 plus 20 is 30.

The totals: 22 chose cat, 28 chose dog, 50 in all.

2 Keep only the given row

Given girl: only this row counts.

The others do not.

In it: 20 chose dog, out of 30.

3 Write the fraction

So the probability is 20/30.

Careful!

The bottom is only the girls: 30.

Not all 50.

4 Simplify

Both 20 and 30 can be divided by 10.

That makes it simpler.

So it is 2/3.

5 Check

Let's check with the rule: the probability of both, divided by the probability of girl.

Both: 20 out of all 50.

Girl: 30 out of 50.

Dividing by a fraction: flip it and multiply.

The 50s cancel: 20/30.

The same.

So the answer is right!

Let's look back.

First: make a table.

Then: keep only the given row.

Then: write the fraction.

Then: simplify.

Last: check.

▶ Watch it solved

Boys 12 cat 8 dog, girls 10 cat 20 dog, P(girl given dog) Medium

The question

Question: People were asked: cat or dog?

12 boys chose cat and 8 chose dog.

10 girls chose cat and 20 chose dog.

One person who chose dog is picked at random.

What is the probability they are one of the girls?

The line means given.

Given they chose dog: we only look at the people who chose dog.

P stands for probability.

The line stands for given.

1 Make a table

One row for each group, one column for each answer, and the totals.

12 boys chose cat, 8 chose dog.

12 plus 8 is 20.

10 girls chose cat, 20 chose dog.

10 plus 20 is 30.

The totals: 22 chose cat, 28 chose dog, 50 in all.

2 Keep only the given column

Given dog: only this column counts.

The others do not.

In it: 20 are girls, out of 28.

3 Write the fraction

So the probability is 20/28.

Careful!

The bottom is only the people who chose dog: 28.

Not all 50.

4 Simplify

Both 20 and 28 can be divided by 4.

That makes it simpler.

So it is 5/7.

5 Check

Let's check with the rule: the probability of both, divided by the probability of dog.

Both: 20 out of all 50.

Dog: 28 out of 50.

Dividing by a fraction: flip it and multiply.

The 50s cancel: 20/28.

The same.

So the answer is right!

Let's look back.

First: make a table.

Then: keep only the given column.

Then: write the fraction.

Then: simplify.

Last: check.

▶ Watch it solved

A bag has 5 red and 3 blue marbles, two are picked without… Harder

The question

Question: A bag has 5 red and 3 blue marbles.

Two marbles are picked, one after the other.

The first one is not put back.

What is the probability the second is blue, given the first is blue?

The line means given.

We already know the first is blue.

P stands for probability.

The line stands for given.

1 Draw a tree

2 Go along the given branch

Given the first is blue: we go along the blue branch only.

3 Read the next branch

From there, blue is the branch with 2/7.

So the probability is 2/7.

One blue is already out of the bag.

Careful!

That is the probability of both.

Here the first is already blue: we only need the second branch.

4 Check

Let's check with the rule: the probability of both, divided by the probability of the first being blue.

Times 3/8, then divided by 3/8: we are back to 2/7.

The same.

So the answer is right!

Let's look back.

First: draw a tree.

Then: go along the given branch.

Then: read the next branch.

Last: check.

▶ Watch it solved