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KiRa [710]
3 years ago
6

3.4.4 Journal: Exponential vs. Quadratic

Mathematics
1 answer:
zysi [14]3 years ago
5 0

Answer:

what's the question your asking for?


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500 - 800 + 60

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Answer:

a) P(  Y^{C} | X ) = 0.180

b) P(Y | X^{C}  ) = 0.998

Step-by-step explanation:

Let

P(X) - Probability that he acts hungry

P(Y) - Probability that he had ate dinner,

Given,

P(X | Y) = 0.5

P(X | Y^{C}  ) = 0.99

P(Y) = 0.9

a.)

P(  Y^{C} | X ) =  \frac{P( X | Y^{C} ). P(Y^{C} )   }{P( X | Y^{C} ). P(Y^{C} ) + P( X | Y ) . P (Y) }

                  = \frac{(0.99)(0.1)}{(0.99)(0.1) + (0.5)(0.9)} = \frac{0.099}{0.549} = 0.180

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b.)

P(Y | X^{C}  ) = \frac{(1 - P(X | Y ) ) . P(Y)}{P( X^{C} )  } =  \frac{(1 - P(X | Y ) ) . P(Y)}{ 1 - P( X )  }

                 = \frac{(1 - 0.5)(0.9)}{1 - [(0.99)(0.1) + (0.5)(0.9) ]} = \frac{(0.5)(0.9)}{1 - [(0.099) + (0.45) ]} = \frac{0.45}{1 - [0.540]} = \frac{0.45}{0.451} = 0.998

⇒P(Y | X^{C}  ) = 0.998

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