Today's LMAD featured a game where a couple could win a car by finding three of a kind from among six playing cards (by choosing only three of them). The six cards consisted of three K's and three 3's.
After the couple chose their three cards, two of them were revealed. Since the producers knew which cards were where, they revealed the pair which the couple was guaranteed to have under the circumstances. The couple was then offered a sure thing to end the deal, rather than being given the chance to switch their final card to one of the other three unrevealed ones.
The questions for your consideration:
1. What was the probability that the third card they chose did in fact make three of a kind?
2. If they could have switched to one of the other three cards, would that probability change, and if so, to what?
And finally:
3. Before revealing the third card the couple chose, the producers revealed a pair from the three unchosen cards (again, this was guaranteed to exist). If the couple were allowed to switch at that point and take the one other unrevealed card, how (if at all) would that affect their probability of winning the car?
Enjoy.