1. An engineering system

Question :
An Engineering system consisting of n components is said to be k-out-of-n system $(k \le n)$ if and only if atleast k of the n components function. Suppose that all components function independently of each other with the probability $\frac{1}{2}$. Find the conditional probability that component 1 is working given that the system funstions, when k=2 and n=3.

If your 2 of 3 system is working, we must be in one of the following cases:

BGG
GBG
GGB
GGG

where G=good (working machine), and B=bad. Isn't the probability that any particular machine is working then 3 of 4?

3. Originally Posted by qmech
If your 2 of 3 system is working, we must be in one of the following cases:

BGG
GBG
GGB
GGG

where G=good (working machine), and B=bad. Isn't the probability that any particular machine is working then 3 of 4?

here's what i could make of the question

The component consist of n components and there probability is $\frac{1}{2}$

ie. $P(x_i) = \frac{1}{2}$ .......where i = 0 ...n components

is there any one who could help me with this question

4. Originally Posted by zorro
here's what i could make of the question

The component consist of n components and there probability is $\frac{1}{2}$

ie. $P(x_i) = \frac{1}{2}$ .......where i = 0 ...n components

is there any one who could help me with this question
Post #2 tells you how to do it (note that each of the outcomes is equally likely). Where are you stuck?

5. Is this correct?

Originally Posted by mr fantastic
Post #2 tells you how to do it (note that each of the outcomes is equally likely). Where are you stuck?

Pr(Component functioning) = $\frac{1}{2}$

Pr(2 out 3 components functioning)= Pr(B) = $\frac{3}{5}$

Pr(1 st component functioning) = Pr(A)= $\frac{1}{2}$

Pr(A|B) = $\frac{Pr(A \cap B)}{Pr(B)}$ = $\frac{Pr(A) . Pr(B)}{Pr(B)}$ = $\frac{\frac{1}{2} . \frac{3}{5}}{\frac{3}{4}}$ = $\frac{2}{5}$

Is this correct?

6. Originally Posted by zorro
[snip]
Find the conditional probability that component 1 is working given that the system funstions, when k=2 and n=3.
Do you mean
Originally Posted by zorro and edited by Mr F
[snip]
Find the conditional probability that component 1 is working, given that the system funstions when k=2 and n=3.
In other words, the system has three components and the given condition is that the system functions when k = 2 and n = 3? This is very different to what you posted.

(Punctuation in the wrong place can completely change the meaning of something ....)

7. Originally Posted by mr fantastic
Do you mean

In other words, the system has three components and the given condition is that the system functions when k = 2 and n = 3? This is very different to what you posted.

(Punctuation in the wrong place can completely change the meaning of something ....)
It is .............

Find the conditional probability that component 1 is working given that the system functions, when k=2 and n=3.

8. The question in the first post is correct

Originally Posted by mr fantastic
Do you mean

In other words, the system has three components and the given condition is that the system functions when k = 2 and n = 3? This is very different to what you posted.

(Punctuation in the wrong place can completely change the meaning of something ....)

The question in the first post is correct, could u please tell me if the answer which i have posted above is correct or no , if not then why is it not correct

9. Originally Posted by zorro
The question in the first post is correct, could u please tell me if the answer which i have posted above is correct or no , if not then why is it not correct
The wording in the first post is ambiguous to me so I can't say.

10. Originally Posted by mr fantastic
The wording in the first post is ambiguous to me so I can't say.
Mr fantastic what should i do with this question ........I need to know whether the answer which i have posted is correct or no?