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Answer :
To solve this problem, we need to calculate the probability that a dormitory resident chosen at random has had a flu shot, given that he is male. We'll use the information provided in the table to find this conditional probability.
Here’s how we can break it down step-by-step:
1. Identify the number of males who had a flu shot:
- From the table, we see that 39 male residents had a flu shot.
2. Identify the total number of males:
- According to the table, there are 51 male residents in total.
3. Calculate the probability:
- The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
- In this case, the probability that a dormitory resident chosen at random has had a flu shot, given that he is male, is the number of males who had a flu shot divided by the total number of males.
[tex]\[
\text{Probability (Had Flu Shot | Male)} = \frac{\text{Number of males who had a flu shot}}{\text{Total number of males}} = \frac{39}{51}
\][/tex]
4. Simplify the fraction (if necessary) or convert it to a decimal:
- When you divide 39 by 51, you get approximately 0.765.
Therefore, the probability that a dormitory resident chosen at random is male and has had a flu shot is approximately 0.765, or 76.5%.
Here’s how we can break it down step-by-step:
1. Identify the number of males who had a flu shot:
- From the table, we see that 39 male residents had a flu shot.
2. Identify the total number of males:
- According to the table, there are 51 male residents in total.
3. Calculate the probability:
- The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
- In this case, the probability that a dormitory resident chosen at random has had a flu shot, given that he is male, is the number of males who had a flu shot divided by the total number of males.
[tex]\[
\text{Probability (Had Flu Shot | Male)} = \frac{\text{Number of males who had a flu shot}}{\text{Total number of males}} = \frac{39}{51}
\][/tex]
4. Simplify the fraction (if necessary) or convert it to a decimal:
- When you divide 39 by 51, you get approximately 0.765.
Therefore, the probability that a dormitory resident chosen at random is male and has had a flu shot is approximately 0.765, or 76.5%.
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