The probability to have an increased blood pressure in a par

The probability to have an increased blood pressure in a particular patients group is p = 0.25 The doctor had 5 patients. Calculate probability to observe exactly patients with increased blood pressure, no more then 2 patents with increased blood pressure 10% of the small town inhabitants are employed at the enriching plant. Professional hazard causes prevalence of pneumonia among plant workers to reach 25 cases per 1000 people in a year, but prevalence in the rest of the townfolk is only 10 cases per 1000 people per year. Caclulate, what is the probability that particular person, suffering pneumonia is working at the plant.

Solution

Probability of increased blood pressure = 0.25
Probability of normal blood pressure= 0.75
Lets any two paient have high blood pressure and 3 have normal so comuulative probability will be = .25^2*.75^3 =.02636
   no more than two blood pressure = 0 blood pressure +1 bp +2 bp = .75^5+.75^4*.25+.02636
  => .3427
N2: probability = 10/1000/(25/1000)= 0.4