At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.06 and the probability that the flight will be delayed is 0.09 . The probability that it will not rain and the flight will leave on time is 0.86 . What is the probability that it is raining and the flight is delayed? Round your answer to the nearest thousandth.

Step 1 ：Given probabilities: \(P(rain) = 0.06\), \(P(delay) = 0.09\), \(P(not\ rain\ and\ on\ time) = 0.86\)

Step 2 ：Calculate \(P(not\ rain) = 1 - P(rain) = 1 - 0.06 = 0.94\)

Step 3 ：Calculate \(P(on\ time) = 1 - P(delay) = 1 - 0.09 = 0.91\)

Step 4 ：Calculate \(P(rain\ and\ on\ time) = P(rain) * P(on\ time) = 0.06 * 0.91 = 0.0546\)

Step 5 ：Calculate \(P(not\ rain\ and\ delay) = P(not\ rain) * P(delay) = 0.94 * 0.09 = 0.0846\)

Step 6 ：Calculate \(P(rain\ and\ delay) = 1 - P(rain\ and\ on\ time) - P(not\ rain\ and\ on\ time) - P(not\ rain\ and\ delay) = 1 - 0.0546 - 0.86 - 0.0846 = 0.0008\)

Step 7 ：\(\boxed{P(rain\ and\ delay) = 0.001}\)