What is the Success Rate of an Overloaded Industrial Hoist?

[korr2221]

An industrial hoist is being used in an emergency job where the weight exceeds the design limits of two of its components. For the amount of weight being lifted, the probability that the upper attachment hook will fail is 0.20. The probability that the lower hook will fail is 0.10. What is the probability that the hoisting job will be successfully complete?

no equations

P(a') = 0.20
P(b') = 0.10
P(a)= 1-0.20 = .80
P(b)= 1-.0.10 = .90

P(a+b)= 0.8 + 0.9 - 0.8*0.9 = 1.7- 0.72 = .98

someone suggested that this problem is indep.
if this is indep

then P(ab) = 0.8*0.9 = 0.72...

can someone review over this and check?

 

[tiny-tim]

hi korr2221!

if they're independent, P(ab) = P(a)P(b)

 

[korr2221]

hi korr2221!

if they're independent, P(ab) = P(a)P(b)

from what I've read it doesn't seem independent...?

 

[tiny-tim]

If they're not independent, the question would have to tell you how they're dependent, and it doesn't.

I think you can safely assume that probabilities are independent unless either the question says they're not, or it's obvious that they're not.