Question

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?

Answer 1

0.33

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:

`P(S10|S5)=(P(S10)*P(S5|S10))/(P(S5))` 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
`P(S10|S5)=(0.2*1)/(0.6)=0.33`