Question

l. The population of a state is divided equally through five main regions A, B, C, D, and E Some of the state residents are foreigners and the rest are local residents. If you know that percentage offoreign residents are 20%, 40%, 10%, 15%, and 25% respectively, what is the probability that a randomly selected resident is local. [6Marks]

Answer 1

P( a randomly selected resident is foreigner)

= P(foreigner | state A) *P(state A) + P(foreigner | state B) *P(state B)+ P(foreigner | state C) *P(state C) + P(foreigner | state D) *P(state D) + P(foreigner | state E) *P(state E)

$= (0.20*\frac{1}{5}) + (0.40*\frac{1}{5}) + (0.10*\frac{1}{5}) + (0.15*\frac{1}{5}) + (0.25*\frac{1}{5})$

$= 0.22$

The probability that a randomly selected resident is local

= 1 - P( a randomly selected resident is foreigner)

= 1 - 0.22

= 0.78 (ans)