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Probabilidades: Conteo, Eventos y Bayes

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Probabilidades: Conteo, Eventos y Bayes

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Quiz de probabilidades y distribución

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Ruth Cumbicos
Ruth Cumbicos
Ecuador

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Probabilidades: Conteo, Eventos y Bayes
 

Probabilidades: Conteo, Eventos y BayesOnline version

Quiz de probabilidades y distribución

by Ruth Cumbicos
1

1) En un conjunto de 4 elementos {A,B,C,D}, ¿cuántas permutaciones distintas se pueden formar con 3 elementos sin repetición?

2

2) Cuántas combinaciones de 5 objetos tomados de 2 en 2 hay?

3

3) En un dado justo de 6 caras, probabilidad de obtener 5 o 6?

4

4) En una urna con 2 rojas y 3 azules, probabilidad de sacar roja dado que se obtuvo azul?

5

5) Si sensibilidad=0.9, especificidad=0.95 y prevalencia=1%, probabilidad de enfermedad dada prueba positiva?

6

6) Una urna tiene 3 blancas y 2 negras. ¿P(blanca)?

7

7) Dos monedas justas, probabilidad de obtener exactamente una cara?

8

8) Permutaciones de A,A,B: ¿cuántas palabras distintas se forman?

9

9) Regla de conteo: 3 opciones en A y 4 en B; cuántas combinaciones?

10

10) Con test de Bayes: prevalencia 2%, FPR 5%, FNR 10%; probabilidad de no tener enfermedad dado negativo?

Explicación

P(4,3)=4×3×2=24; las demás son conteos no permutaciones o subutilizados.

Combinaciones: C(5,2)=5×4/2=10; evita contar orden.

Existen 2 resultados favorables de 6 posibles; 2/6=1/3.

P(roja|azul)=2/(2+3)=2/5; evita usar no condicionada.

P(D|+)=0.01×0.9 / (0.01×0.9+0.99×0.05) ≈ 0.154.

Suma total 5, tres son blancas.

Caso independiente: 2×(1/2)×(1/2)=1/2.

Permutaciones con repetición: 3!/2!=3.

Regla del producto: 3×4=12.

P(not D|−)=0.98×0.95 / (0.98×0.95 + 0.02×0.10) ≈ 0.999.

 
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