The Correct Answer and Explanation is:
The correct answer is 13/17.
This question asks for a conditional probability. The key phrase “given that he is male” tells us that we are not considering all 100 surveyed residents. Instead, our focus is restricted to only the male residents in the group. This condition changes the total number of possible outcomes for our calculation.
First, we need to determine the total size of this new, restricted group. By looking at the provided table, we can find the total number of male residents surveyed. We look at the “Male” column and go down to the “Total” row. The table shows this number is 51. This value will be the denominator of our probability fraction, as it represents the entire population we are now considering.
Next, we need to find the number of individuals within this specific group who meet the desired criterion, which is having received a flu shot. We stay within the “Male” column and find the number in the “Got Flu Shot” row. The table indicates that 39 males received a flu shot. This number represents the favorable outcomes, so it becomes the numerator of our fraction.
With these two numbers, we can set up the probability. The probability is the number of males who got a flu shot divided by the total number of males. This gives us the fraction 39/51.
Finally, this fraction can be simplified to its lowest terms. Both the numerator, 39, and the denominator, 51, are divisible by 3. Dividing 39 by 3 gives us 13, and dividing 51 by 3 gives us 17. Therefore, the simplified probability that a randomly selected resident has had a flu shot, given that the resident is male, is 13/17.
