Here is a probability system
The probability of failure of #1=0.1, #2=0.2,#3=0.3,#4=0.4
Now im trying to find the probability that the system works..
I so far have 1∩(2U4)∩3 which seems right but I dont know what numbers to plug in and whether to add or multiply
Also, I need to find the prob. that at most 3 events of these components work.
Then, using conditional prob. I can't seem to find the prob. that the system works given that at most 3 of the components work..
Im so lost
Hello, mightydog78!
Here is a probability system
The probability of failure of #1 = 0.1, #2 = 0.2,#3 = 0.3,#4 = 0.4
(a) Now im trying to find the probability that the system works.
(b) Also, I need to find the prob. that at most 3 of these components work.
(c)Then, using conditional prob. I can't seem to find the prob. that
. . the system works, given that at most 3 of the components work.
. .
(a) The system works if:
. . [1] #1 works, #2 works, #3 works, and #4 works.
. . . .
. . [2] #1 works, #2 works, #3 works, and #4 fails.
. . . .
. . [3] #1 works, #2 fails, #3 works, and #4 works.
. . . .
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
(b) The opposite of "at most 3 components work" is "4 components work."
. .
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
The numerator is [2] and [3] in part (a):
. .
. .
Hence, the numerator is: .
And we found the denominator in part (b): .
Therefore: .