What is the Success Rate of an Overloaded Industrial Hoist?

In summary, the probability of successfully completing the hoisting job is 0.98, based on the probabilities of the upper and lower attachment hooks failing, which are 0.20 and 0.10 respectively. Assuming the probabilities are independent, the probability of both hooks failing is 0.72.
  • #1
korr2221
20
0
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?
 
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  • #2
hi korr2221! :smile:

if they're independent, P(ab) = P(a)P(b) :wink:
 
  • #3


tiny-tim said:
hi korr2221! :smile:

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

from what I've read it doesn't seem independent...?
 
  • #4
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.
 

What does it mean for probabilities to be independent?

When probabilities are independent, it means that the outcome of one event does not affect the probability of the other event occurring. In other words, the probability of both events happening together is equal to the product of their individual probabilities.

How do you calculate the probability of independent events?

To calculate the probability of independent events, you simply multiply the probabilities of each event together. For example, if you roll a die and flip a coin, the probability of rolling a 3 and flipping heads is 1/6 * 1/2 = 1/12.

Can independent events have a correlation?

Yes, independent events can have a correlation. This means that although the events are not dependent on each other, they may still have some relationship or influence on each other. This is different from the concept of independence, where the outcome of one event does not affect the probability of the other event occurring.

What is the difference between independent and mutually exclusive events?

Independent events have no effect on each other, while mutually exclusive events cannot occur at the same time. In other words, if one event happens, the other event cannot happen. For example, getting a heads on a coin toss and getting a tails on the same toss are mutually exclusive events.

Can dependent events ever be considered independent?

No, dependent events cannot be considered independent. If the outcome of one event affects the probability of the other event occurring, they are not independent. For example, drawing a red card from a deck and then drawing another red card without replacement are dependent events, as the probability of drawing a red card changes after the first draw.

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