|The probability that a certain kind of component will survive a shock test is 3/4. Find the probability that exactly 2 of the next 4 components tested survive. : Assuming that the tests are independent and p = 3/4 for each of the 4 tests, we obtain 32 (1) 3 b( 2; 4, 4! 27 4 2! 2! 44 128 Example 5.7: The complexity of arrivals and departures of planes at an airport is such that computer simulation is often used to model the "ideal" conditions. For a certain airport with three runways, it is known that in the ideal setting the following are the probabilities that the individual runways are accessed by a randomly arriving commercial jet: Runway 1: Runway 2: Runway 3: Pi = 2/9, P2 = 1/6, P3 = 11/18. What is the probability that 6 randomly arriving airplanes are distributed in the following fashion? Runway 1: Runway 2: Runway 3: Solution: Using the multinomial distribution, we have 2 airplanes, 1 airplane, 3 airplanes 2 1 11 6. 3 11 f( 2, 1, 3: %3D 9'6'18' ,3, 18 6! 22 1 113 = 0.1127. 2! 1!3! 92 6 183