Question on Statistics (maths)?

Question

Question on Statistics:

Ok, a bag has 5 marbles in it. One marble is red, Four marbles are blue.

Each time you take out a marble, you do not look at what colour it is. You do not return it to the bag.

At the moment, the chances of pulling out the red marble are 1 in 5.

What are the chances of pulling out the red marble, if, each time you take a marble, the colour of the marble stays unknown, and the number of the marbles in the bag is reduced by 1 each time.

Eg:

5 Marbles in bag: 1 in 5 chance. (marble is not seen or replaced)

4 Marbles in bag: ...??...chance (marble is not seen or replaced)

3 Marbles in bag: ...??...chance (marble is not seen or replaced)

etc...

etc...

Please note that this isn't a homework assignment, I am past my schooling years :)

Your help is greatly appreciated, thankyou to all who answer.

Answer 1

There is a hard way and an easy way to do this.  You can use logic to see that regardless of what happens on previous draws, your chance is always going to be 1/5 to pick the red marble (up to the 5th draw) because you don't have any information about the previous draws.

This can also be done using conditional probability (Bayes' rule).

For example, with 4 marbles in the bag, you calculate the probability that you pick a red marble given that a red marble was picked on the first draw and the probability that you pick a red marble given that a blue marble was picked on the first draw and then weight these probabilities by the probabilities of picking a red on the first draw and blue on the first draw, respectively.

i.e.  Pr (red with 4 marbles in bag) =

Pr (red with 4 marbles in bag | red on first draw)*Pr (red on first draw) +

Pr (red with 4 marbles in bag | blue on first draw)*Pr (blue on first draw)

= (0/4)*(1/5) + (1/4)*(4/5) = 1/5.

The same method can be applied to future draws from the bag.

Answer 2

It is still a 1 in 5 chance because as you draw the marbles, they remain unknown so they don't effect the probability.