161142

There is a 1/7 chance that the first ball goes in the middle and whenever this happens we win. There is a further 1/6 chance that the second ball lands in the middle. This too guarantees a win. To calculate The chance that 2 balls are next to each other we first must calculate the chance of it happening if both balls land outside the center. No matter where the first ball lands (outside the center) there are 5 places the second ball can land. If it goes in two of these you win. This means that the chance of winning when it lands outside is 2/5. But since only 29/42 of the time you don’t get a middle the chance you win by to outside balls is 58/210 add that to the 65/210 that comes from having one in the center the probability of winning is 123/210 or 41/70.