Question

Obesity is a growing public health concern worldwide. Adults with a high body mass index (BMI)

of 25 or greater are considered overweight or obese. The table shows the number of adults (in

millions) who are overweight or obese in countries with different income levels, based on data

from the World Health Organization and the United Nations.

Country income level	Millions with high BMI	MIllions with low BMI	Total
High	549	414	963
Upper middle	612	1042	1654
lower middle	288	1083	1371
low	63	357	420
all	1512	2896	4408

(a) What is the probability that a randomly selected adult has a high BMI?

(b) Given that a randomly selected adult is from a lower middle-income country, what is the

probability the adult has a low BMI?

(c) What is the probability a randomly selected adult either has high BMI or comes from a low-income

country?

(d) What is the probability that a randomly selected adult either has low BMI or comes from a

high-income country?

(e) Are the events having high BMI and having low BMI mutually exclusive?

(f) Are the events coming from a high-income country and having low BMI independent?

Answer 1

• The Total population = 4408 Million.
• Population with High BMI =1512 Million

(a) probability that a randomly selected adult has a high BMI = 1512/4408=0.34 Answer

(b)

Given that a randomly selected adult is from a lower middle-income country, the

probability the adult has a low BMI = 1083/1371=0.78 answer

(c)Probability of the randomly selected adult either has high BMI or comes from a low-income

A = High BMI;p(A) = 1512/4408=0.34

B = Low Income;P(B) = 420/4408 =0.09

P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) =0.34+0.09-.014 =0.416 Answer

(d)

Probability of the randomly selected adult either has low BMI or comes from a high-income

P(Low BMI ∪ high Income) = P(Low BMI)+ P(High Income)- P(Low BMI ∩ high Income)

=0.65+0.21-0.09

=0.77 Answer

(e)

YES

Two events (or propositions) are defined as mutually exclusive or disjoint when they cannot both occur at the same time

Hence high BMI and having low BMI are mutually exclusive

(f) yes they are

Independent Events are not affected by previous events.

high-income country and having low BMI independent