Originally Posted by

**luke95** This is a fun question i found on the internet, a bit harder than my course and ive spent hours on it but cant find a solution, i was hoping someone could help me.

Here's the situation.

You are in jail and have been sentenced to death tomorrow, however there's a way out.

you're given 12 red balls and 12 blue balls with 2 urns, you have to fully distribute the balls between these two urns. the executioner will then select an urn and draw a ball

if it is blue you live and if it is red you die.

suppose you place k balls in to the first urn and 24-k in to the second

suppose you put i blue balls in to the first urn and 12-i in to the second

Let A be the event that you live.

By conditioning on the urn that the executioner chooses, and using the law of total probability show that:

P(A) = (12i - ki + 6k) / k(24-k)

please could you explain the steps used so i can try and understand the solution and method.

Thank you in advance

Luke