I'm a little strapped for time for this question (and a few others), as I've got a midterm for my statistics course in a week and I'm already a good deal behind on the course material (due to an early sickness in the term). Any help on this would be greatly appreciated.
Be sure to read the question carefully.
A train of wagons transports hazardous materials. Each wagon, and independently from the others, has a probability to be defective. Prior to the train's departure all wagons are examined by two inspectors who do not exchange their inspection's results during the control. We assume that each inspector will detect a default on a given wagon (if any) with probability . One default is enough to delay the train's departure (for repair). Compute the following probabilities:
a) The train's departure will be delayed.
b) The train will leave with at least one wagon defective.
c) Compute the numerical values of the probabilities in a) and b) when and .