What is the probability of at most 25 and exactly 25 with examples?
Answers
In a group of 40 people, 10 are healthy and every person the of the remaining 30 has either high blood pressure, a high level of cholesterol or both. If 15 have high blood pressure and 25 have high level of cholesterol,
a) how many people have high blood pressure and a high level of cholesterol?
If a person is selected randomly from this group, what is the probability that he/she
b) has high blood pressure (event A)?
c) has high level of cholesterol(event B)?
d) has high blood pressure and high level of cholesterol (event A and B)?
e) has either high blood pressure or high level of cholesterol (event A or B)?
f) Use the above to check the probability formula: P(A or B) = P(A) + P(B) - P(A and B).
a) Let x be the number of people with both high blood pressure and high level of cholesterol. Hence (15 - x) will be the number of people with high blood pressure ONLY and (25 - x) will be the number of people with high level of cholesterol ONLY. We now express the fact that the total number of people with high blood pressure only, with high level of cholesterol only and with both is equal to 30.
(15 - x) + (25 - x) + x = 30
solve for x: x = 10
b) 15 have high blood pressure,hence P(A) = 15/40 = 0.375
c) 25 have high level of cholesterol, hence P(B) = 25/40 = 0.625
d) 10 have both,hence P(A and B) = 10/40 = 0.25
e) 30 have either, hence P(A or B) = 30/40 = 0.75
e) P(A) + P(B) - P(A and B) = 0.375 + 0.625 - 0.25 = 0.75 = P(A or B)