1. ## Probability

An urn contains 3 blue and 7 red marbles. Marbles are drawn, one at a time, without replacement from the urn. Explain why the probability of that the third marble drawn is red, is equal to the probability of the first marble drawn is red.

2. Originally Posted by requal
An urn contains 3 blue and 7 red marbles. Marbles are drawn, one at a time, without replacement from the urn. Explain why the probability of that the third marble drawn is red, is equal to the probability of the first marble drawn is red.
Draw a tree diagram and use it to calculate the probability of each event.

3. So there is no distinct reason why the probabilities of drawing red on the first or the third are the same? I don't think it is just a coincidence?

4. Originally Posted by requal
So there is no distinct reason why the probabilities of drawing red on the first or the third are the same? I don't think it is just a coincidence?
A tree diagram will make any deep reason for this clear.

5. okay, i've drawn a tree diagram, I dont see any patterns whatsoever? Perhaps someone can tell me?

6. Nice question requal

Consider 10 boxes in which you are going to put the marbles that you

select i.e one box for each marble.The first marble getting into the first

box,2nd marble getting into the second box and ...so on.

Now it is clear that the probability of red marble getting into any box is 3/10.

7. Hello, requal!

Another way of looking at the problem . . .

An urn contains 3 blue and 7 red marbles.
Marbles are drawn, one at a time, without replacement from the urn.
Explain why the probability of that the third marble drawn is red,
is equal to the probability of the first marble drawn is red.

Considering only the colors of the marbles,
. . they can be drawn in $\displaystyle {10\choose3,7} \:=\:120$ ways.

Imagine listing the 120 possible orders.

In how many of them is the third marble red?

It should be no surprise to us that: .$\displaystyle \begin{array}{c}\text{the third marble is red }\frac{7}{10}\text{ of the time} \\ \\[-4mm] \text{the third marble is blue }\frac{3}{10}\text{ of the time}\end{array}$