Question

QUESTION 1. On average, one in every 1000 people living in a city is known to have cancer. In a study carried out in this province, 5000 people were checked for health. According to this;
a) Calculate the probability that 7 out of 5000 people will get cancer.
b) Calculate the probability that no more than 1 person out of 5000 can get cancer.

Answer 1

Given,

Average number of people having cancer in every 1000 people = 1

Average number of people having cancer in every 5000 people = 5

X : Number of people out of 5000 people will get cancer

X follows Poisson distribution with = 5

Probability mass function of X is given by

Probability that 'x' number of people out of 5000 people will have cancer = P(X=x)

a) Probability that 7 out of 5000 people will get cancer = P(X=7)

Probability that 7 out of 5000 people will get cancer = 0.1044

b)  probability that no more than 1 person out of 5000 can get cancer = P(X1) = P(X=0)+P(X=1)

P(X=0)+P(X=1) = 0.006737947+0.033689735 = 0.0404276820.0404

probability that no more than 1 person out of 5000 can get cancer =0.0404