You have a standard pack of 52 playing cards. You then shuffle them and begin to draw out cards until you have three of a kind. What is the most likely number of cards drawn when this happens?
You then shuffle another pack of 52 playing cards into the pile. What happens to the expected number of cards now? (i.e. does it double / halve / stay the same?)
(In reply to simulation
Thanks Charlie! (Though, I can't believe you stooped to using a computer to solve the problem!)
Anyway... would you like to change your 4's to 8's, and your 52's to 104's... and run the program again (to simulate the two deck question).
The mode will stay around 14, probably moving to 13. And the 50% mark will also stay around where it is... moving a little bit towards the front (towards the lower numbers).
BTW, you didn't calculate where the '50% mark' is... :-)
Edited on November 19, 2003, 4:47 pm