Probability - Conditional Probability

\(3\) out of \(8\) vehicles on the road speed up when the amber light is flashed. If a sample of \(25\) cars are selected at random, determine the probability that

1. At most \(10\) vehicles speed up when the amber light is flashed.
2. At most \(10\) vehicles speed up when the amber light is flashed given that more than \(4\) vehicles speed up when the amber light is flashed.
3. At least \(6\) of the samples have at least \(10\) vehicles speed up when the amber is flashed, given that \(17\) such samples are taken.