Since playing cards is very popular during the Diwali festival, here is a special probability puzzle with cards, contributed by Alok Mittal from his Mathematical Circles class. I heard this one last night and could not resist. I am breaking the puzzle into three different difficulty levels, please exercise your judgment when sharing with your children.
(1) You pick three cards of the same suite, say Spade of 2, 3 and 4. Put them all face down and shuffle them. Now pick one card at a time. What is the probability that Spade of 3 is picked in the end?
(2) You take all the cards of the same suite, lets say Spade again. Ace is considered the smallest and King the largest. You draw three cards at random in the sequence. What is the probability that the value of the third one lies in between the first two?
(3) You take all the 52 cards and draw three cards at random like last time. How would the probability differ from #2, considering that cards of same denomination are considered equal regardless of the suite and the outcome you want is that the third card is strictly inbetween the first two cards and not equal to either of them.
As always, please send your answers directly to me at firstname.lastname@example.org. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.
Happy playing with cards!