A professor wanted to know more about media consumption habits among the students in his class. He took note of each student's gender ("Male" or "Female") and asked the student which communication platform they used most often (either "Telegram" or "Whatsapp"). It was found thatrate(Male | Telegram) > rate(Male | Whatsapp). Which of the following statements must be true?(I) rate(Telegram | Male) > rate(Telegram | Female).(II) rate(Female | Telegram) < rate(Female | Whatsapp).(III) rate(Whatsapp | Female) < rate(Whatsapp | Male).
Question
A professor wanted to know more about media consumption habits among the students in his class. He took note of each student's gender ("Male" or "Female") and asked the student which communication platform they used most often (either "Telegram" or "Whatsapp"). It was found thatrate(Male | Telegram) > rate(Male | Whatsapp). Which of the following statements must be true?(I) rate(Telegram | Male) > rate(Telegram | Female).(II) rate(Female | Telegram) < rate(Female | Whatsapp).(III) rate(Whatsapp | Female) < rate(Whatsapp | Male).
Solution
Para resolver esta pregunta, primero definamos las tasas mencionadas:
- rate(Male | Telegram): La proporción de hombres que usan Telegram.
- rate(Male | Whatsapp): La proporción de hombres que usan Whatsapp.
- rate(Telegram | Male): La proporción de usuarios de Telegram que son hombres.
- rate(Telegram | Female): La proporción de usuarios de Telegram que son mujeres.
- rate(Female | Telegram): La proporción de mujeres que usan Telegram.
- rate(Female | Whatsapp): La proporción de mujeres que usan Whatsapp.
- rate(Whatsapp | Female): La proporción de usuarios de Whatsapp que son mujeres.
- rate(Whatsapp | Male): La proporción de usuarios de Whatsapp que son hombres.
Sabemos que rate(Male | Telegram) > rate(Male | Whatsapp). Esto significa que, entre los hombres, una mayor proporción usa Telegram en comparación con Whatsapp.
Ahora evaluemos cada una de las afirmaciones:
(I) rate(Telegram | Male) > rate(Telegram | Female): Esta afirmación no necesariamente debe ser verdadera. La proporción de hombres que usan Telegram puede ser mayor que la de mujeres que usan Telegram, pero esto no implica directamente que la proporción de usuarios de Telegram que son hombres sea mayor que la proporción de usuarios de Telegram que son mujeres.
(II) rate(Female | Telegram) < rate(Female | Whatsapp): Esta afirmación tampoco necesariamente debe ser verdadera. La proporción de mujeres que usan Telegram puede ser menor que la de mujeres que usan Whatsapp, pero esto no se deduce directamente de la información dada.
(III) rate(Whatsapp | Female) < rate(Whatsapp | Male): Esta afirmación no necesariamente debe ser verdadera. La proporción de usuarios de Whatsapp que son mujeres puede ser menor que la proporción de usuarios de Whatsapp que son hombres, pero esto no se deduce directamente de la información dada.
Por lo tanto, ninguna de las afirmaciones (I), (II) o (III) debe ser necesariamente verdadera basándose únicamente en la información proporcionada.
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