In the year 2003, the population of a certain district was 1.8 million. Thirty percent of the population was in the age group 15-40 years. In the same year, 120,000 people in the district the Voluntary Counseling and Testing (VCT) contra for an HIV test. If a person was selected at random from the district in this year. Find the probability that the person visited a VCT centre and was in the age group 15- 60 years.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
.30 * 120,000/1,800,000 = .30 * 12/180 = ?
To find the probability that a person visited a VCT center and was in the age group 15-40 years, we need to determine the number of people who visited a VCT center and were in that age group, and then divide it by the total population.
Step 1: Calculate the number of people in the age group 15-40 years.
Given that 30% of the population was in this age group and the population of the district in 2003 was 1.8 million, we can calculate the number of people in the age group 15-40 years as follows:
30% of 1.8 million = (30/100) * 1.8 million = 0.3 * 1,800,000 = 540,000
Step 2: Calculate the number of people who visited a VCT center.
Given that 120,000 people visited a VCT center, this is the number we'll use.
Step 3: Calculate the number of people who visited a VCT center and were in the age group 15-40 years.
To find this, we need to find the intersection of the two groups, which means the number of people who satisfy both conditions. In this case, it's the number of people in the age group 15-40 years who visited a VCT center. Since there is no specific number provided for this intersection, we'll assume that all the people who visited a VCT center were in the age group 15-40 years. Therefore, this number is 120,000.
Step 4: Calculate the probability.
The probability of a person visiting a VCT center and being in the age group 15-40 years is the ratio of the number of people who satisfy both conditions to the total population. Therefore, the probability is:
(120,000 / 1,800,000) = 0.0667 (rounded to four decimal places) or 6.67% (rounded to two decimal places).
Therefore, the probability that a person visited a VCT center and was in the age group 15-40 years is approximately 0.0667 or 6.67%.