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Suppose that the probability of surviving for 5-years after being diagnosed with a particular cancer is 0.60; and the probability of surviving for 10 years is 0.20. If a person survives 5 years, what is the probability that she will survive 10 years?

Respuesta :

dogacandu

Answer:

0.33

Step-by-step explanation:

Let P(S10) be the probability that surviving for 10-years after being diagnosed with a particular cancer

And P(S5) be the probability that surviving for 5-years after being diagnosed with a particular cancer

We have

P(S5)=0.6 and P(S10)=0.2

And we have the conditional probability equation:

[tex]P(S10|S5)=\frac{P(S10)*P(S5|S10)}{P(S5)}[/tex] where

  • P(S10|S5) is the probability that surviving for 10-years after being diagnosed with a particular cancer given that survived for 5-years after being diagnosed with a particular cancer
  • P(S5|S10) is the probability that surviving for 5-years after being diagnosed with a particular cancer given that survived for 10-years after being diagnosed with a particular cancer (which is 1 because if you survived 10 years, you already survived 5 years)

Then [tex]P(S10|S5)=\frac{0.2*1}{0.6}=0.33[/tex]

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