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Given: p(e) = 0.42, p(f) = 0.51, and p(e ∪ f) = 0.70 part
a.find p(e ∩ f). part
b.find p(e | f). part
c.find p(f | e). part
d.are the events e and f independent?

Respuesta :

LammettHash
[tex]\mathbb P(E\cap F)=\mathbb P(E)+\mathbb P(F)-\mathbb P(E\cup F)=0.42+0.51-0.70=0.23[/tex]

[tex]\mathbb P(E\mid F)=\dfrac{\mathbb P(E\cap F)}{\mathbb P(F)}=\dfrac{0.23}{0.51}\approx0.45[/tex]

[tex]\mathbb P(F\mid E)=\dfrac{\mathbb P(F\cap E)}{\mathbb P(E)}=\dfrac{0.23}{0.42}\approx0.55[/tex]

[tex]E[/tex] and [tex]F[/tex] are not independent. Independence would require that [tex]\mathbb P(E\cap F)=\mathbb P(E)\times\mathbb P(F)[/tex], but [tex]0.42\times0.51\approx0.27\neq0.23[/tex].

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