Parallel systems that are independent!!!

[nicoledawn]

This one is kinda long, but really really tricky!!!! Much guidance needed!!!

Components in a system are said to be in parallel if the system fails only if all the components in the system fail. ex: if we have an alarm warning system that gives warnings via flashing light, a siren and a digital display, the warning sytem fails only if all three devices fail to alert people to the problem.

i) suppose that the light fails with probability 0.01, the siren with probability 0.02 and siplay wtih the probability 0.08. Assuming failures occurs independently, what is the probability that the system fails?

heres what i did: A=light, B=Siren and C=display

pr(A, B, and C)=pr(a)*pr(b)*pr(c)
=(0.01)(0.02)(0.08)
=0.00016
so the probability of the system that fails is 0.00016?

I totally think i did this wrong, so please if you could tell me what i should do instead would be awesome!

 

[tkhunny]

Except for changing from A, B, C to a, b, c, I don't see the problem. Why do you doubt?

 

[nicoledawn]

thanks!
Im just not confident in math, and Im doing a stat university course at home, rather than in a classroom, and the text book is confuising me, so I am doubting all my answers. thanks so much!