Hi all, I have a question here that I remain puzzled
about.
I have difficulties coming up with a probability tree that gives
me the answer that is correct.. Will appreciate any help!
Question:
In a city, 70% of the children get their recommended
immunisation for a disease. Past data show that with the
immunization, boys have 3% chance of contracting the disease while
girls have only 2% of contracting the disease. For children without
the immunization, they (irrespective of genders, which are assumed
to be equal) would have 15% chance of contracting the disease.
Determine the following:
a) Be a girl without the immunisation and does not contract the
disease [0.128]
b) Be a child who had the immunisation but contracted the
disease [0.018]
(there are parts after b but I should be able to get them done
once I know the correct probability tree diagram...)
So far what I've tried is to stem from children with and without
the immnunization, then to children who contracted the disease /
who did not contracted the disease, and then lastly to girls/boys.
I tried using algebra (i.e. prob of contract disease despite
immunised to be a and if otherwise, 1-a, and so on for girls/boys)
and simultaneous equations afterwhich to solve the question, but
did not manage to get the answer.
With and without Immunisation ==> Boy/Girl ==> Contract or
didn't contract disease
a) 0.3 X 0.5 X 0.85 = 0.1275, round up to 3 decimal places =
0.128
b) Split into two parts, girls and boys. We will handle girls
first, then boys.
For girls: 0.7 X 0.5 X 0.02 = 0.007
For boys: 0.7 X 0.5 X 0.03 = 0.0105
Total = 0.007 + 0.0105 = 0.0175, round up = 0.018