28 Ryder Cup miracle in golf. The Ryder Cup is a three-day golf tournament played between a team of golf professionals from the United States and a team from Europe. A total of 28 matches are played between the teams; one point is awarded to the team winning a match and half a point is awarded to each team if the match ends in a tie (draw). The team with the most points wins the tournament. In 1999, the United States was losing 10 points to 6 when it miraculously won 8.5 of a possible 12 points on the last day of the tournament to seal the win. On the last day, 12 single matches are played. A total of 8.5 points can be won in a variety of ways, as shown in the accompanying table. Given one team scores at least 8.5 points on the last day of the tournament, Chance (Fall 2009) determined the probabilities of each of these outcomes assuming each team is equally likely to win a match. Let x be the points scored by the winning team on the last day of the tournament when the team scores at least 8.5 points. Find the probability distribution of x .

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Wins Ties Points Probability 596 6 7 7 7 8 9 10 10 10 11 11 12 75634512340123012010 8.5 .000123 5 8.5 .008823 9.0 .000456 8.5 .128030 9.0 .020086 5 9.5 .001257 8.5 .325213 9.0 .153044 9.5 .032014 10.0 .002514 9.0 .115178 9.5 .108400 10.0 .032901 10.5 .003561 10.0 .034552 10.5 .021675 11.0 .003401 11.0 .006284 11.0 .001972 12.0 .000518