A friend randomly chooses three different numbers and writes each one on a separate 3 × 5 card. The cards are placed face down on the table in front of you. Your goal is to choose the card with the largest number.
The Rules: You start by turning over any card and looking at the number written on it. If you think that the card you have turned over contains the largest number, you are done; this is your card. However, if you think there is a larger number on one of the two remaining cards, you can discard your frst selection, pick up another card and look at the number written on it. If you think this is the largest number, you keep this card, and the game is over. If you decide that this isn’t the largest number, you throw away the card you’re holding and make the third card yours. Develop a strategy that will maximize the probability that you end up with the card with the largest number. For example, if your strategy is “keep the frst card you turn over,” the probability that you have the largest number is 1/3.