1. Identify the number of males who had a flu shot: 39.
2. Identify the total number of males: 51.
3. The probability that a randomly chosen male had a flu shot is the number of males who had a flu shot divided by the total number of males: \(\frac { 39} { 51} \).
4. Simplify the fraction: \(\frac { 39} { 51} = \frac { 39} { 51} \times \frac { 80} { 80} = \frac { 39} { 80} \).

Supplemental Knowledge

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is a fundamental concept in statistics and probability theory. The formula for conditional probability is:
\[P( A| B) = \frac { P( A \cap B) } { P( B) } \]
Where:

• \(P( A| B) \) is the probability of event A occurring given that event B has occurred.
• \(P( A \cap B) \) is the probability of both events A and B occurring.
• \(P( B) \) is the probability of event B occurring.
  In this context, we are interested in finding the probability that a dormitory resident has had a flu shot given that he is male.

Knowledge in Action

Imagine you are attending a college campus during flu season and there is concern over an outbreak. Your health services director needs to know how effective their flu shot campaign has been among different groups; by understanding conditional probabilities they can better target interventions; for example if more males than expected have not received flu vaccination, more focus may need to be put towards encouraging males to receive vaccination.
Companies often utilize conditional probabilities as part of their marketing strategies to determine customer likelihood to purchase certain items based on prior purchases or demographic information, helping tailor marketing efforts more efficiently.

Understanding concepts like conditional probability can significantly enhance your analytical skills and decision-making abilities. If you're eager to delve deeper into such fascinating topics, UpStudy offers comprehensive resources tailored just for you. From live tutor sessions to AI-powered problem-solving tools, UpStudy ensures you grasp these concepts thoroughly.
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