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