Problem 13STE

Balls are randomly removed from an urn that initially contains 20 red and 10 blue balls.

(a) What is the probability that all of the red balls are removed before all of the blue ones have been removed? Now suppose that the urn initially contains 20 red, 10 blue, and 8 green balls.

(b) Now what is the probability that all of the red balls are removed before all of the blue ones have been removed?

(c) What is the probability that the colors arc depleted in the order blue, red, green?

(d) What is the probability that the group of blue balls is the first of the three groups to be removed?

Solution:

Step 1 of 4:

- An urn contains 20 red and 10 blue balls and the balls are removed randomly.

The claim is to find the probability that all of the red balls are removed before all of the blues have been removed.

Then P(last removed ball is blue) =

=

= 0.3333

Hence, the probability that all of the red balls are removed before all of the blues has been removed is 0.3333.