Let E and F are events of a experiment such that P(E) = 3/10 P(F) = ½ and P(F|E) = ⅖. Find the value of (i) P(E ∩ F) (ii) P(E|F) (iii) P(E U F)

Question

Let E and F are events of a experiment such that P(E) = 3/10 P(F) = ½ and P(F|E) = ⅖. Find the value of (i) P(E ∩ F) (ii) P(E|F) (iii) P(E U F)
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Solution 1

Claro, vamos a resolver el problema paso a paso.

Dado:

  • ( P(E) = \frac{3}{10} )
  • ( P(F) = \frac{1}{2} )
  • ( P(F|E) = \frac{2}{5} )

(i) Para encontrar ( P(E \cap F) ):

Sabemos que ( P(F|E) = \frac{P(E \cap F)}{P(E)} ).

Entonces, [ \frac{2}{5} = \frac{P(E \cap F)}{\frac{3}{10}} ]

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