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Answer :
Sure! To find the probability that a randomly chosen male dormitory resident has had a flu shot, we can follow these steps:
1. Identify the relevant data: We are interested in the male residents who had flu shots. From the table, we see that:
- There are 39 male residents who had flu shots.
- The total number of male residents is 51.
2. Understand the concept of conditional probability: We want to find the probability that a dormitory resident has had a flu shot given that the resident is male. This is known as conditional probability.
3. Set up the probability formula: The probability of an event, given some condition, is calculated as the number of favorable outcomes divided by the total number of possible outcomes under that condition. In this case, it's the number of males who had a flu shot divided by the total number of males.
4. Calculate the probability:
[tex]\[
\text{Probability} = \frac{\text{Number of males who had a flu shot}}{\text{Total number of males}} = \frac{39}{51}
\][/tex]
5. Simplify the fraction (if possible): The fraction [tex]\(\frac{39}{51}\)[/tex] simplifies to approximately 0.7647 when converted to a decimal.
Therefore, the probability that a randomly chosen male dormitory resident has had a flu shot is approximately 0.7647, which can be expressed as 76.47% if converted to a percentage.
1. Identify the relevant data: We are interested in the male residents who had flu shots. From the table, we see that:
- There are 39 male residents who had flu shots.
- The total number of male residents is 51.
2. Understand the concept of conditional probability: We want to find the probability that a dormitory resident has had a flu shot given that the resident is male. This is known as conditional probability.
3. Set up the probability formula: The probability of an event, given some condition, is calculated as the number of favorable outcomes divided by the total number of possible outcomes under that condition. In this case, it's the number of males who had a flu shot divided by the total number of males.
4. Calculate the probability:
[tex]\[
\text{Probability} = \frac{\text{Number of males who had a flu shot}}{\text{Total number of males}} = \frac{39}{51}
\][/tex]
5. Simplify the fraction (if possible): The fraction [tex]\(\frac{39}{51}\)[/tex] simplifies to approximately 0.7647 when converted to a decimal.
Therefore, the probability that a randomly chosen male dormitory resident has had a flu shot is approximately 0.7647, which can be expressed as 76.47% if converted to a percentage.
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