Problem 2770. Probability of Choosing a Red Ball

Given two jars of red and blue balls, find the probability of choosing a red ball from Jar 1 after going through the steps.

Step 1: Choose a random ball from Jar 2 and add it to Jar 1

Step 2: Choose a random ball from Jar 1

Step 3: Calculate the probability of the final ball being red

Example:

Given inputs for Jar 1 and Jar 2

Jar 1: (r1,b1) = (2,7)

Jar 2: (r2,b2) = (5,5)

Choose a ball from Jar 2 and add it to Jar 1.

   _Note: Jar 1 could now have either 3 blue and 7 red or 2 blue and 8 red._ 

Taking into consideration both possibilities, the likelihood of the final ball being red is 0.25 .