Question

The table below shows the sugar contents in an individual of different age groups, where below $100$ mg/dl is considered as safe, between $100$ and $125$ mg/dl is considered at risk but not called as diabetic, and above $125$ mg/dl is stated as diabetic.

Age Group	< 100mg/dL	100-125mg/dL	>125	Total
18-25	9	22	17	48
26-35	16	48	34	98
36-45	19	35	40	94
Older than 45	12	27	21	60
Total	56	132	112	300

Based on the table, if a single participant is selected at random from all participants, what is the probability that he or she will be at risk for diabetes and be at least $36$ years old?

• A. $\frac{7}{60}$
• B. $\frac{11}{25}$
• C. $\frac{31}{77}$
• D. $\frac{31}{150}$

Answer 1

Answer: (D)

$\frac{31}{150}$

The number of people falling in the range of $100-125$ and having an age of $36$ years or above is $35+27=62$.

Now the total number of people is $300$.

Thus the required probability is

$=\frac{62}{300}=\frac{31}{150}$

That is roughly equal to $20.67\%$.