In a shop, people can take chewing gum from a dispenser on the right, or the left. The dispenser on the right has 7 packets of mint gum, and 3 packets of fruit gum, and the dispenser on the left has 7 packets of mint gum and 7 packets of fruit gum. What is probability of taking packet of mint gum?

My solution: 1/2 * 7/10 + 1/2 * 7/14 = 12/20, but correct answer is 14/24. Can you explain me why?