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Homework Statement
what is the probability that a component which is still working after 800 hrs, will last for at least 900hrs
Homework Equations
conditional probability
P(E|A) = ( P( E ∩ A) ) / ( P(A) )
The Attempt at a Solution
Im just checking my own understanding if this problem is conditional probability or not.I alraedy asked my teacher about the correct answer and I apparently had the correct answer.
But I was asked by my classmates to explain the answer, and I wasnt sure how deeply I understood the problem.
Looking at the table provided, we can see component lifetimes.
To my mind the problem can be translated into conditional probability terms such as:
"given that the component has lifetime from 800 upwards, what is probability that the component has lifetime from 900 upwards"
E : survive900hrsOrMore: (210+820) /1500 ==0,686666
A : survive800hrsOrMore: (210+820+240) /1500 == 0,846666
P(E|A) = P(E∩A) / P(A)
P(A) was calculated to be 0,846666
I think the probability of the intersection happening can be seen from the intersection in the following picture.
P(E∩A) was to my understanding calculated thusly:
(820+210)/1500 =0,686666
FavorableCases/ totalSampleSpace
in this case FavorableCases = 1030 parts that are inside the intersection
I don't know if this intersection probability can be calculated with a formula, but that seems to be how to calculate the probability of the intersection happening.
thus answer is
0,686666/ 0,846666= 0,811023