And chance drawing another blue ball

Solved Step by Step With Explanation- Expected value of X

Questions

Solved Step by Step With Explanation- Expected value of X

Answer

In this case, you have a 2/6 chance of drawing a different colored ball on the first trial (white or blue) and a 4/6 chance of drawing another red ball.

So, E(1) = 1 + (2/6 * 1 + 4/6 * (1 + E(1))) = 1 + (1/3 + 4/3 * E(1))

In this case, you have a 4/6 chance of drawing a different colored ball on the first trial (red or white), which ends the sequence, and a 2/6 chance of drawing another blue ball, which takes you back to the beginning.

So, E(3) = 1 + (4/6 * 1 + 2/6 * E(1)) = 1 + (2/3 + 1/3 * E(1))

We can solve this system of equations to find E(1):

E(1) = 1 + (1/3 + 4/3 * E(1))

So, the expected value of X when starting with 1 red ball (n = 1) is 2.

Now, we can calculate EX, the overall expected value:

EX = 1 + 1.5

EX = 2.5