KöMaL 2021 C1683

Ann and Bo are playing the following game on squared sheets of paper. Each player marks a $10\times10$ square on her own sheet of squared paper. In this large square, they colour seven $1\times1$ lattice squares blue, and another 14 lattice squares red. The players cannot see each other's coloured squares. The game starts by Ann naming a pair of numbers $(i,j)$ where $1 \le i,j \le 10$ are positive integers. (For example, $(5,2)$ means the lattice square at the intersection of row 5 and column 2 of the $10\times10$ square.) If the pair $(i,j)$ determines a coloured field on Bo's sheet of paper then Bo will answer hit'', otherwise she will say no hit''. Then the game continues by switching roles: Bo names a pair of numbers and Ann answers. What is the probability that in the third round of the game Ann will hit a blue square and Bo will hit a red square provided that in the first two rounds neither Ann nor Bo had any hits?