Question

13. The arrivals and departures of planes at an airport is such that computer simulations is often used to model the "Ideal" conditions. For Newark airport with three runways, it is known that in the ideal setting, the probabilities that individual runways are accessed by a randomly arriving commercial jet. Runway 1: p1 =1/3. Runway 2: p2 = 7/15 and Runway 3:p3 = 1/5, what is the probability of 10 randomly arriving planes are distributed as Runway 1: 3, Runway 2: 6, Runway 3: -1

Answer 1

Answer:

Given,

n = 10

p1 = 1/3

p2 = 7/15

p3 = 1/5

Here it is a multinomial distribution

i.e.,

P(x1 = 3 , x2 = 6 , x3 = 1) = (10! / 3!*6!*1! ) * p1^3*p2^6*p3^1

substitute p1,p2,p3 values in above expression

= (10! / 3!*6!*1! ) * (1/3)^3 * (7/15)^6 * (1/5)^1

= 840*0.037*0.01033*0.2

= 0.0642