Of all airline flight requests received by a certain discount ticket broker, 90% are for domestic travel (D) and 10% are for international flights (I). Let x be the number of requests among the next three requests received that are for domestic flights. Assuming independence of successive requests, determine the probability distribution of x. (Hint: One possible outcome is DID, with the probability (0.9)(0.1)(0.9)

Given that of all airline flight requests received by a certain discount ticket broker, 90% are for domestic travel (D) and 10% are for international flights (I).

Let x be the number of requests among the next three requests received that are for domestic flights.

X can take values as 0,1, 2 or 3.

Since independence of successive requests is assumed we find that X having two outcomes and independence

X is binomial with n =3 and p= 0.90 (constant for each trial)

PDF of X would be

[tex]P(X=x) = 3Cx (0.9)^r (0.1)^{3-r} , r=0,1,2,3[/tex]

Thus pdf of X is

X 0 1 2 3

p 0.001 0.027 0.243 0.729