3 and 4 go together

3) In a factory, there are 100 new cars produced. Three of the cars have serious defects. The quality control group is going to select 10 cars at random and check them thoroughly. (Each car has same probability than the others to get selected). If in the ten controlled cars they find at least one with a defect, they will control the whole group of 100. What is the probability that they will end up checking the whole bunch? (We assume that when they check a defect car, they always discover that the car is defect.) 4) (This problem is difficult). Same problem as before. But this time when they check a defect car, they only have a probability of 2/3 of discovering the defect. We assume that when they of the others. check several defect cars, each defect car has probability of 2/3 to get detected independently