In a hybrid truss structure, made of steel and wood elements, we want to check their...

Question

Question

In a hybrid truss structure, made of steel and wood elements, we want to check their stress state. Elements can be either in

Answer 1

Answer #1

a) Using the given infromation we have

P(C)=0.65 , P(T)=1-P(C)=1-0.65=0.35

P(S|C)=0.30 and P(S|T)=0.60

b) By total probability theorem we get

$P(S)=P(T)P(S|T)+P(C)P(S|C)\\ ~~~~~~~~~~~~=0.35 (0.60)+ 0.65(0.30) \\ ~~~~~~~~~~~~=0.405$

c) By Bayes theorem we get

The required probability is

$P(T|S)={P(T)P(S|T)\over P(S)} \\ ~~~~~~~~~~~~~~~={0.35 (0.60)\over 0.405} \\ ~~~~~~~~~~~~~~~\approx 0.5185$

d) From the given information we have

P(M)=0.25

$P(M| S\cap C)=0.90$

Since

$P(S|C)={P(S\cap C)\over P(C)} \\ \Rightarrow P(S\cap C)=0.65 \times 0.30=0.195$

Hence,

$P(M| S\cap C)= {P(M\cap S\cap C)\over P(S\cap C)} \\ \Rightarrow P(M\cap S\cap C)=0.90 \times 0.195=0.1755$

e) By Definition of conditional probability

The required probability is

$P( S\cap C|M)= {P(M\cap S\cap C)\over P(M)} \\ ~~~~~~~~~~~~~~~~~~~~~~~={0.1755\over 0.25}\\ ~~~~~~~~~~~~~~~~~~~~~~~=0.702$

Answer 2