Question

In the polya process, what is the probability of drawing a blue ball on each of your first two draws? (assume that you start with one blue ball and one red ball in the urn.)

Answer 1

Answer:

In polya process ,if the urn contains p one color balls and q another color balls and If you have drawn a ball of one color suppose red then the same color ball is replaced in the bag.

Now, coming to the question

In the urn = 1 Blue ball + 1 Red ball

Total number of balls = 2

Favorable cases= 1 blue ball

Probability of an event  $=\frac{\text{total favorable outcome}}{\text{total possible outcome}}$

Probability of drawing blue ball in first draw $=\frac{1}{2}$

Now, the drawn ball is replaced by same color ball in the urn.

So, again probability of drawing blue ball in second draw as the urn has one blue ball and one red ball  $=\frac{1}{2}$.

As, drawing blue balls in each of two draws is an independent event.

So, required probability $=\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}$