A rental truck agency services its vehicles on a regular basis, routinely checking for mechanical problems. Suppose that the agency has six moving vans, two of which need to have new brakes. During a routine check, the vans are tested one at a time.
a. What is the probability that the last van with brake problems is the fourth van tested?
b. What is the probability that no more than four vans need to be tested before both brake problems are detected?
c. Given that one van with bad brakes is detected in the first two tests, what is the probability that the remaining van is found on the third or fourth test?