Question

Within a group of elderly human subjects, 35% of the population was diagnosed with diabetes, 56% was obese, and 15% was both obese and affected by diabetes.

1. What would be the probability that a person known to be obese is also affected by diabetes?

1. 0.18                 b) 0.27                         c) 0.43                         d) 0.89

2. What would be the probability that a person known to be obese is NOT affected by diabetes?

1. 0.43                 b) 0.67                         c) 0.73                         d) 0.89

3. According to the information provided, are obesity and diabetes independent events?

1. Yes                  b)   No                         c) Undetermined                    d) Sometimes

Answer 1

Solution:

Given ,

P(D) = 35% = 0.35

P(O) = 56% = 0.56

P(D O) = 15% = 0.15

a)

P(D | O)

= P(D O) / P(O)

= 0.15 / 0.56

= 0.27

b)

P(D^c | O)

= P(D^c O) / P(O)

= [P(O) - P(D O) ] / P(O)

= [0.56 - 0.15 ] / 0.56

= 0.73

c)

P(D) * P(O) = 0.35 * 0.56 = 0.196

P(D O) = 0.15

P(D O)   P(D) * P(O)

Not independent

Correct option is

No