Final answer:
The probability of being older than 25 years and having a hemoglobin level above 11 is approximately 35.9%. The probability of having a hemoglobin level above 11 is also approximately 35.9%. Being older than 25 years and having a hemoglobin level above 11 are independent events according to the given data.
Step-by-step explanation:
To find the probability of being older than 25 years and having a hemoglobin level above 11, we need to look at the table given. We can see that there are 429 total individuals, and out of those, 154 have a hemoglobin level above 11 and are older than 25 years. Therefore, the probability is 154/429, which simplifies to approximately 0.359, or 35.9%.
The probability of having a hemoglobin level above 11 can be found by summing up the number of individuals in the table who have a hemoglobin level above 11, regardless of their age. From the table, we see that there are 154 individuals with a hemoglobin level above 11. Therefore, the probability is 154/429, which simplifies to approximately 0.359, or 35.9%.
Whether being older than 25 years and having a hemoglobin level above 11 are dependent on each other can be determined by comparing the joint probability (both events happening together) with the product of the individual probabilities. If the joint probability is close to the product of the individual probabilities, then the events are considered to be independent. However, if the joint probability is significantly different from the product of the individual probabilities, then the events are dependent on each other.
Since the probability of being older than 25 years and having a hemoglobin level above 11 is 0.359 (35.9%) and the product of the individual probabilities (probability of being older than 25 years multiplied by the probability of having a hemoglobin level above 11) is 0.353 (35.3%), we can see that the joint probability is very close to the product of the individual probabilities. Therefore, we can conclude that being older than 25 years and having a hemoglobin level above 11 are independent events.