Question

A cross-sectional survey was conducted on adults (³20 years of age) residing in the Khairpur district in Sindh province of Pakistan. One objective of the survey was to evaluate the relationship of social economic position with under- and overweight. The following table gives the frequency counts for the number of participants in socioeconomic status (low, median, high) and BMI for a random sample of 1000 participants.

Social Economic Class	Underweight	Normal	Overweight/Obese	Total
Low	36	128	39	203
Median	87	352	160	599
High	22	94	82	198
Total	145	574	281	1,000

1) what is the probability that a randomly selected participant is both Normal (A) and falls in the Median social economic class (B)?

- step-by-step explanation on excel if possible and/or formula write out

2) what is th probability that a randomly selected participant is either Overweight/obese (A) or falls in the low level social economic class (B)?

- step-by-step explanation on excel if possible and/or formula write out

3) Suppose a randomly selected participant is form the Low Social Economic Class (A). Given this knowledge what is the probability that this person is overweight (B).

- step-by-step explanation on excel if possible and/or formula write out

4) Is being overweight (A) independent of social economic class? Consider the case of whether or not a randomly selected participant falls in the Low Social Economic Class (B) to answer this question?

- step-by-step explanation on excel if possible and/or formula write out

Answer 1

(1) P(Normal and falls in the Median social economic class)

Let A: Participant is normal

B: Participant falls in the social economic class

P(A and B)

According to the table there are 352 participant which are normal as well as they are falls in the social economic class and total 1000 participants are there.

Therefore, the probability that a randomly selected participant is both Normal (A) and falls in the Median social economic class (B) is 0.352

(2) P(participant is either Overweight/obese or falls in the low level social economic class)

Let A: Participant is overweight

B: Falls in low level social economic class

The formula to find the Union that is OR probability is,

Plug all the values in the formula,

Therefore, the probability that a randomly selected participant is either Overweight/obese (A) or falls in the low level social economic class (B) is 0.445

(3) P(participant is form the Low Social Economic Class, Given this knowledge what is the probability that this person is overweight) that is P(B | A)

Let A: Participant is from the low economic class

B: Person is overweight.

The formula to find the conditional probability is,

P(A and B) and P(A) are already calculated in b part,

Plug both the probabilities in the formula of conditional probability,

Therefore, the probability that this person is overweight given that a randomly selected participant is form the Low Social Economic Class is 0.192

(4) Independence:

Two events are independent when their joint probability becomes the product of their marginal probability that is

If A and B are independent then P(A and B) = P(A) * P(B)

Let A: Overweight

B: Participant fall in low Social economic class.

P(A and B), P(A) and P(B) are alraedy calculated in the previous parts,

which is not P(A and B) that is 0.039

Therefore,

Therefore, both the events overweight and low social economic class are not independent.