Small electrical motors are shipped in lots of 50. Before such a shipment is accepted an inspector chooses 5 motors at random and tests them. If none of the motors are found to be defective, the shipment is accepted. If one or more are found to be defective, then the entire shipment is tested (all 50 motors). Suppose that it is known that there are 3 defective motors in the lot. Suppose it costs $100 to test a motor.
What is the expected cost for any given shipment?
What is the expected cost until a shipment is accepted?
My friend and I are doing this to prep for our midterm and we can't come up with how to calculate the p values for p(x=0) and p($x\geq 1)$
We're super lost please walk us through this
Five motors are chosen out of $50$ for testing. If none of the defective ones is chosen, all must be chosen from the $47$ good ones. The probability that no defective motor is chosen for testing is $${{47\choose5}\over{50\choose5}}$$