Question

In a faraway land, there are 72% white people. There are 30% of people have a particular disease. And if you randomly select a person, that person has 20% chance of being white and have the disease. (a) What proportion of students are non-white and who is healthy? (b) Kelly’s race is white, what is the chance that she has this disease? (c) Are the events of being white and having the disease independent events? (d) If you randomly select 10 people, what is the chance that 2 have the disease?

Answer 1

Explanation:

Let the probability of people being white be P ( W ) and being diseased

be P ( D )

Given

P ( W ) = .72 , P ( D ) = .3

P ( W∩D ) = .2

a )

P (
`W^c` ∩
`D^c` ) = P
`( WUD)^c` = 1 - P ( W U D )

= 1 - [ P( W ) + P ( D ) - P ( W ∩ D ) ]

= 1 - ( .72 + .3 - .2 ) = .18

b )

P ( D / W ) = P ( W∩D ) / P(W) = .2 / .72 = .27778

c )

No , because

P ( W∩D ) = .2

p ( W) x P ( D ) = .72 x .3 = .216

so P ( W∩D ) is not equal to P ( W) x P ( D )

d )

We shall apply binomial distribution

chance = 10C₂ x .3² ( 1 - . 3 )⁸