cap_3_mont_p_57

OK PUNTOS 0.8

=CAPITULO 3, PROBLEMA 57=

Suponga que P(A|B) = 0.2, que P(A|B') = 0.3 y que P(B) = 0.8. ¿Cuál es la P(A)?

__**Solución:**__



math P\left ( A\mid B \right ) = 0.2 math math P\left ( A\mid B' \right ) = 0.3 math math P\left ( B\right ) = 0.8 math math P\left ( A\right ) = ? math math P\left ( A\mid B \right ) = \frac{P\left ( A\cap B \right )}{P\left ( B \right )} math math P\left ( A\cap B \right ) = P\left ( A\mid B \right )P\left ( B \right ) = (0.2)(0.8) = 0.16 math math P\left ( A\mid B' \right ) = \frac{P\left ( A\cap B' \right )}{P\left ( B' \right )} = \frac{P\left ( A \right ) - P\left ( A\cap B \right )}{1-P\left ( B \right )} math

Entonces:

math 0.3 = \frac{P\left ( A \right ) - P\left ( A\cap B \right )}{1-P\left ( B \right )} math math 0.3 - 0.3P\left ( B \right ) = P\left ( A \right ) - P\left ( A\cap B \right ) math math 0.3 - 0.3\left ( 0.8 \right ) = P\left ( A \right ) - 0.16 math math 0.3 - 0.24 + 0.16 = P\left ( A \right ) math math P\left ( A \right ) = 0.06 + 0.16 math math P\left ( A \right ) = 0.22 math

Solucionado por:


 * Cristian Eduardo Polo C.
 * Héctor Julio Rivera A.
 * Felipe Uribe C.