@sandy111,
If you are trying to compute the probability of
not solving the problem, there is no difference between them working sequentially or in parallel - they all must still fail to solve the problem. That's why you approach problems like this from the fail perspective instead of the pass perspective. If you want to do it the much harder way, it looks like this:
P = A + A'B + A'B'C
P = 2/3 + (1/3)(5/7) + (1/3)(2/7)(1/10) = 64/70