The lifetime of a device behaves according to the probability law P(t, infinity) = 1/(1+t) , t 0
a. calculate the probability that the lifetime of the device is greater or equal than 3 but less than 8
b. Calculate the probability that the device last at least another 5 hours given that it has already lasted 5.

Question

The lifetime of a device behaves according to the probability law P(t, infinity) = 1/(1+t) , t >0 
a. calculate the probability that the lifetime of the device is greater or equal than 3 but less than 8 
b. Calculate the probability that the device last at least another 5 hours given that it has already lasted 5.

anonymous · Answer

ok that was way way wrong, sorry

anonymous · Answer

embarrassingly wrong

anonymous · Answer

but fortunately the answer is much much easier
the probability that the life is greater than 3 is $p(3)=\frac{1}{1+3}=\frac{1}{4}$
the probability it is greater than 8 is $p(8)=\frac{1}{9}$ so the probability it is greater than 3 and less than 9 is $\frac{1}{4}-\frac{1}{9}$

anonymous · Answer

second one

$$P(A|B)=\frac{P(A\cap B)}{P(B)}$$  
$$P(B)=p(5)=\frac{1}{6}$$ and 
$$P(A \cap B)=\frac{1}{6}-\frac{1}{11}$$

einstein · Answer

Here probability is a continuous function of time and you are applying discrete formulas

anonymous · Answer

formula is the same

einstein · Answer

oh ya, thaks ,good work

einstein · Answer

I also have a probability problem would you like to solve that Mr. satellite73