Answer to Question #173659 in Statistics and Probability for Funmi

Question

1.In a group of 40 subjects screened for non- communicable diseases, 10 are healthy and every person of the remaining 30 has either high blood pressure, a high level of cholesterol or both. You were further informed that 27 have high blood pressure and 25 have a high level of cholesterol.

ii. If a person is selected randomly from this group of subjects, what is the probability that he or she has either high blood pressure or high level of cholesterol?

2. In a group of 60 subjects screened for non- communicable diseases, 20 are healthy and every person of the remaining 40 has either high blood pressure, a high level of cholesterol or both. You were further informed that 15 have high blood pressure and 25 have a high level of cholesterol. If a person is selected randomly from this group of subjects, what is the probability that he or she has either high blood pressure or high level of cholesterol or both using the additive rule of probability.

Answer 1

Solution:

(1): Notations:

S - number of persons taken in a group.

H - number of healthy persons.

NH - number of non-healthy persons.

BP - number of non-healthy persons having high blood pressure.

C - number of non-healthy persons having a high level cholesterol.

$n(S)=40,n(H)=10,n(NH)=30 \\n(BP)=27,n(C)=25$

${Now}, n(NH)=n(BP)+n(C)-n(BP\cap C) \\\Rightarrow30=27+25-n(BP\cap C) \\\Rightarrow n(BP\cap C)=22$

$Now, n(BP\cup C)=(27-22)+(25-22)=5+3=8$

So, required probability$=\frac8{40}=0.2$

(2): $n(S)=60,n(NH)=n(BP\cup C)=40$

Required probability$=\frac{40}{60}=\frac23$