An urn has r red and w white balls that are randomly

Step 1 of 3

Given an urn has ‘r’ red and ‘w’ white balls that are randomly removed one at a time.

Let denotes the event that the  ball removed is red.

Our goal is

We need to find :

a). P().

b). P().

c). P().

P() =

P() =

P() =

P() =

P() =

P() =

P() =  

P() =

P() =

P() =

\(\mathrm{P}\left(R_{3}\right)=\left(\frac{r-2}{r+w-2}\right) \times \frac{r \times r}{(r+w)^{2}}+\left(\frac{r-1}{r+w-2}\right) \times \frac{r \times w}{(r+w)^{2}}+\left(\frac{r-1}{r+w-2}\right) \times \frac{r \times w}{(r+w)^{2}}+\left(\frac{r-1}{r+w-2}\right) \times \frac{w^{2}}{(r+w)^{2}}\)

P() =

P() =

P() =

Similarly P() =

Therefore, P() =.