Question

A taxi cab company has 12 ambassadors and 8 fiats. If 5 of these taxi cabs are in the workshop for repair and an ambassador is as likely to be in for repair as a fiat, what is the probability that (i) 3 of them are ambassadors and 2 are fiats, (

Answer 1

Let X means the number in the workshop out of the 5 taxi cabs.

we note that N=20, k=12, and n= 5 X follows a hyper geometric distribution given by  

P(X=r)= 12Cr * C5-R/20C5  

r =0,1…,5

(i) 3 of them are ambassadors and 2 are fiats,

P(3 ambassadors and 2 fiats)=12C3*8C2/20 C5

220*28/15504=385/969