A gambler presents you with an even-money wager. You will roll two dice, and if the highest number showing is one, two, three or four, then you win. If the highest number on either die is five or six, then she wins. Should you take the bet?
Instead of six possibilities, there are now 36. You can make a simple grid to see your odds of winning, with the six possible results for the first die forming the columns, and the six possible results for the second die forming the rows. As you can see, your odds of winning are 16 out of 36, or 4/9, so you should not take the bet.
Remember, if a five or a six shows on either die, the gambler wins. So with two dice, you have to win on both at once, which is harder. The odds of winning with one die are 2/3, so another way to figure the odds of winning on both dice at once is to multiply the probabilities: 2/3 times 2/3 equals 4/9.