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Objetivo: Realizar el cálculo de los ejercicios sobre teorema de bayes y probabilidad de suma de cada uno de los ejercicios mostrados

The problem presented is a probability problem involving sets, where we are given percentages of people using different types of transportation (public, private, or both). Let’s break it down:

### Given information:
- \( P(A) \) = 70% = Probability of using public transportation.
- \( P(B) \) = 55% = Probability of using private transportation.
- \( P(A \cap B) \) = 40% = Probability of using both types of transportation.

### Task:
Calculate the probability that someone uses at least one type of transportation, meaning public or private or both.

This can be calculated using the inclusion-exclusion principle:

\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]

### Substituting the given values:

\[
P(A \cup B) = 0.70 + 0.55 - 0.40 = 0.85
\]

So, the probability that a person uses either public, private, or both types of transportation is **85%**.

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Would you like further details on any part of this problem? Here are five related questions for practice:

1. What is the probability that a person uses only public transportation?
2. What is the probability that a person uses only private transportation?
3. What is the probability that a person does not use any transportation?
4. How does the inclusion-exclusion principle work in set theory?
5. Can you visualize the problem using a Venn diagram?

**Tip:** Always check if there is overlap (both events happening) when calculating probabilities using the union formula.

En una encuesta realizada en una ciudad acerca del medio de transporte usado, se encontró que el 70% usan servicios públicos, el 55% usan servicio particular y el 40% usa los dos tipos de transporte. Calcule la probabilidad de que se use algún tipo de transporte.

En este ejercicio, calculamos la probabilidad de que una persona use servicios públicos, privados o ambos, utilizando el principio de inclusión-exclusión. Dado que el 70% usa transporte público, el 55% usa privado, y el 40% usa ambos, la probabilidad total es 85%.

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