You are playing a game of bingo with friends. In this game, balls are labeled with one of the letters of the word BINGO and a number. Some of these letter-number combinations are written on a bingo card in a 5 × 5 array, and as balls are randomly drawn and announced, players mark their cards if the ball’s letter-number combination appears on the cards. The first player to complete a row, column, or diagonal on a card says “Bingo!” and wins the game. In the game you’re playing, there are 20 balls left. To complete a row on your card, you need N-32 called. To complete a column, you need G-51 called. To complete a diagonal, you need B-6 called.
What is the probability that the next two balls drawn do not have a letter-number combination you need, but the third ball does?
