Question

Ten new buildings are being inspected for code violations. From past experience, the inspection company estimates that half of all buildings will have code violations.

a: The inspection company randomly inspects four buildings. What is the probability that all four will have code violations?

b: How many of the ten buildings should you expect to have code violations?

Answer 1

it is hypergeometric distribution          
Sample size,     n =    4
No. of events of interest in population    , k = 0.5*10 = 5
Population size   , N =   10

P(X=x) =C(k,x)*C(N-k,n-x)/C(N,n)

a)

here ,x=4

P( X =   4   ) = C(    5   ,   4   ) * C (    5   ,    0   ) / C (    10   ,   4   )=0.0238

b)

expected code voilations = E(X) = n(k/N) =4*5/10 = 2 building