# Question 7d52b

May 18, 2017

After Jeannie picked a green marble, the bag contains 5R 6G 4B.

#### Explanation:

So there are 5R on a total of 15.

So $P \left(red\right) = \frac{5}{15} = \frac{1}{3}$

May 18, 2017

$P \left(R E D\right) = \frac{1}{3}$

#### Explanation:

It is exactly because of this uncertainty that we have a probability topic in maths. There are very few things in life which we know FOR SURE are going to happen. We have to consider that some events are MORE LIKELY to happen, while others are LESS LIKELY to happen. The measure of this chance of something happening is called its probability.

If you toss a coin you cannot predict what the outcome will be, but we know there are only 2 options - head and tails.

If you guess 'heads' before every throw, you will be right about half the time, and wrong half the time.
The chance of a head is 1/2 = 0.5 = 50%
The chance of a tail is 1/2 = 0.5 = 50%#

In this example, we obviously do NOT KNOW which colour marble Eva will pick, but we should realise that some colours are MORE LIKELY to be picked than others.

If there were 9 red marbles and only 1 blue marble in a bag, you would be pretty lucky to choose the blue one without looking. There are 9 times as many reds as the blue.

In this example there were $16$ marbles to start with:

$5$ red, $7$ green, $4$ blue.

Therefore a green is MORE LIKELY to be picked because there are more greens than the others. IN fact, Jeannie picked a green.
The fraction of green was $\frac{7}{16}$, this is also called the probability.

Now the numbers change:

Now there are $15$ marbles because Jeannie keeps her green one.
There is one less marble, and one less green marble.
$5$ red, $6$ green, $4$ blue.

Now we can ask, what is the CHANCE that Eva's marble will be red?

What fraction of the marbles are red? $\frac{5}{15}$

This simplifies to $\frac{1}{3}$

As a guess we could then say that, of every three marbles chosen, we expect that ONE will be red.