Question

# A survey is applied to the inhabitants of a city to determine which public works to choose. Option "construction of a bridge" or "construction of social housing". The results were: 20% of those surveyed chose "construction of a bridge", 16% chose "construction of social housing" and 1% chose both options. IF A RESPONDENT IS RANDOMLY SELECTED WHO CHOSE "Construction of a bridge", what is the probability that he/she also chose the option "construction of social housing"? Justify your answer.

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## Answer to a math question A survey is applied to the inhabitants of a city to determine which public works to choose. Option "construction of a bridge" or "construction of social housing". The results were: 20% of those surveyed chose "construction of a bridge", 16% chose "construction of social housing" and 1% chose both options. IF A RESPONDENT IS RANDOMLY SELECTED WHO CHOSE "Construction of a bridge", what is the probability that he/she also chose the option "construction of social housing"? Justify your answer.

Brice
4.8
1. Denote the events:
- P: "construcción de un puente"
- VS: "construcción de viviendas sociales"

2. Find the given probabilities:
- P$P$ = 0.20
- P$VS$ = 0.16
- P$P \cap VS$ = 0.01

3. Apply the conditional probability formula:
P$VS|P$ = \frac{P$P \cap VS$}{P$P$}

4. Substitute the values:
P$VS|P$ = \frac{0.01}{0.20} = 0.05

5. Conclusion: The probability that an individual who selected "construcción de un puente" also selected "construcción de viviendas sociales" is
0.05

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