“Si se elige uno de los que…” cambia el denominador: solo cuenta ese grupo.
Estrategia paso a paso
Rodea en la tabla la fila o columna del grupo condicionante antes de dividir.
Trampas habituales
Usar el total general como denominador en una probabilidad condicionada.
Ejemplo resuelto
De 30 alumnos que estudian francés, 12 son de 10.º → P(10.º, sabiendo que estudia francés) = $\frac{12}{30}=\frac{2}{5}$.
Preguntas de ejemplo
Intenta responder antes de abrir la solución. Las preguntas están en el idioma del examen.
Pregunta 1
Dificultad fácil≈ 1 min
A bag contains $4$ red marbles, $6$ blue marbles, and $5$ green marbles. If one marble is selected from the bag at random, what is the probability that it is blue?
AA. $\frac{1}{15}$
BB. $\frac{1}{3}$
CC. $\frac{2}{5}$
DD. $\frac{2}{3}$
Ver respuesta y explicación
Respuesta correcta: C. $\frac{2}{5}$
Explicación
There are $4+6+5=15$ marbles, and $6$ are blue, so the probability is $\frac{6}{15}=\frac{2}{5}$.
$\frac{1}{3}$ treats the three colors as equally likely. $\frac{2}{3}$ compares blue marbles with the $9$ marbles that are not blue. $\frac{1}{15}$ is the probability of selecting one particular marble.
Pregunta 2
Dificultad media≈ 1 min
An integer from $1$ to $30$, inclusive, is selected at random. What is the probability that the integer is a multiple of $4$ or a multiple of $6$, or both?
Respuesta numérica (escribes el número).
Ver respuesta y explicación
Respuesta: 1/3 · .3333
Explicación
Multiples of $4$: $4, 8, 12, 16, 20, 24, 28$ ($7$ numbers). Multiples of $6$: $6, 12, 18, 24, 30$ ($5$ numbers). The numbers $12$ and $24$ are in both lists, so there are $7+5-2=10$ numbers. The probability is $\frac{10}{30}=\frac{1}{3}$.
Counting $12$ and $24$ twice gives $\frac{12}{30}$, which is too large.
Pregunta 3
Dificultad difícil≈ 2 min
A playlist contains only jazz songs and pop songs. If a song is selected at random from the playlist, the probability that it is a jazz song is $\frac{3}{8}$. After $12$ pop songs are added to the playlist, the probability that a song selected at random is a jazz song is $\frac{1}{4}$. How many songs were on the playlist before the pop songs were added?
Respuesta numérica (escribes el número).
Ver respuesta y explicación
Respuesta: 24
Explicación
Let $n$ be the original number of songs. There are $\frac{3}{8}n$ jazz songs, and this number does not change. After the pop songs are added there are $n+12$ songs, so $\frac{\frac{3}{8}n}{n+12}=\frac{1}{4}$. Cross-multiplying: $\frac{3}{2}n=n+12$, so $\frac{1}{2}n=12$ and $n=24$.
Check: the playlist had $\frac{3}{8}(24)=9$ jazz songs out of $24$. After $12$ pop songs are added, $9$ of the $36$ songs are jazz, and $\frac{9}{36}=\frac{1}{4}$.
$36$ is the number of songs after the pop songs are added, and $9$ is the number of jazz songs.