Problem with independent events in possibilities

[maria papadakh]

Summary:: problem with independent events in possibilities

A forest has a fire per year with probability 30% and it has 2 fires per year with possibility 5%.The probability of 3 or more fires is 0%.The forest might have disasters from the wind which blows with probability of 100% or has disasters from the fire with probability 25%.If the disasters from the wind are independent from the disasters caused by the fire ,then find the probability of the disasters in the forest per year . I think that P(D)=P(D/W)*P(W)+P(D/F)*P(F) , but I'm not sure for that and I don't know how to use the fact that the distasters of the wind are independent from the disasters caused by the fire .Any ideas, please ??
Where :F1: the event of one fire
F2: the event of two fires
F: the event of fire
D: the event of disasters
W: the event of the wind*PS : I think that the events might be the above.

 

[FactChecker]

For two independent events, A and B, P(A or B) = P(A)+P(B)-P(A and B) = P(A)+P(B)-P(A)P(B)
(The first equality is always true and the second is a consequence of A and B being independent.)

 

[Office_Shredder]

To be honest I don't understand the question. What does it mean the forest has disasters from the wind which blow with probability 100%?

 

[maria papadakh]

hi,finally it was wrong the propability of the wind.it is ten per cent.Can you help me now please?

 

[FactChecker]

This looks like a homework problem, in which case you need to use the correct format and show your work. We can only give guidance and hints.

 

[maria papadakh]

I think that P(D)=P(D/W)*P(W)+P(D/F)*P(F) =P(D/W)0,1+0,25*0,35
P(F)=P(F1)+P(F2)=0,3+0,05=0,35
i don't know how to find P(D/W)

 

[PeroK]

I think that P(D)=P(D/W)*P(W)+P(D/F)*P(F) =P(D/W)0,1+0,25*0,35
P(F)=P(F1)+P(F2)=0,3+0,05=0,35
i don't know how to find P(D/W)

It's not clear to me what probabilities you are trying to calculate. What is P(D) here?

 

[maria papadakh]

it is the posibility of the disasters that happen in a forest.you can read the hole problem above.thank you.

 

[FactChecker]

The problem statement seems to be:
The probability of disaster from wind is 10% and the probability of disaster from fire is 25%. The wind and fire probabilities are independent. What is the combined probability of at least one disaster in a year?
That means that some of the information in the original post is not needed. Have I interpreted this correctly? If so, how would you solve this problem?

 

[maria papadakh]

As the problem is written i think that P(D/F) and P(D/W) are independent
P(D/FUD/W)=P(D/F)+P(D/W)-P(D/F)*P(D/W)=O,1+0,25-O,1*0,25=0,35-O,O25=0,325
Now i think that it might be the solution.Is it right?Do you mean that the P(F1)=0,3 and P(F2) are not need to solve the problem?

 

[FactChecker]

As the problem is written i think that P(D/F) and P(D/W) are independent
P(D/FUD/W)=P(D/F)+P(D/W)-P(D/F)*P(D/W)=O,1+0,25-O,1*0,25=0,35-O,O25=0,325
Now i think that it might be the solution.Is it right?Do you mean that the P(F1)=0,3 and P(F2) are not need to solve the problem?

That is one guess. Is the statement of the problem in the original post exactly correct? The 100% became 10%. Are there other mistakes or things not mentioned? Some of it is still vague.

 

[maria papadakh]

it was corrected some hours ago.there are not other changes.But i think that i miss something.Why P(F1)=0,3 and P(F2)=0,05 are given?

 

[FactChecker]

it was corrected some hours ago.there are not other changes.But i think that i miss something.Why P(F1)=0,3 and P(F2)=0,05 are given?

That is for you to tell us. That is why I suspect that the problem statement is not exact.

 

[haruspex]

Seems to me there is a piece of information missing.
For any given year, we are given the probabilities of one fire and two fires, and we are given the probability that any given fire or high wind event leads to a disaster. What is missing is the probability of a high wind event.

 

[maria papadakh]

or the possibility of 0,1 =P(W) and P(D/F)=O,25 and from the fact that P(D/W) and P(D/F) are independent we could calculate P(D/W)

 

[haruspex]

or the possibility of 0,1 =P(W) and P(D/F)=O,25 and from the fact that P(D/W) and P(D/F) are independent we could calculate P(D/W)

P(W)=0.1? Where did you get that from?
We are given P(D|W)=1.

 

[maria papadakh]

yes,forget this idea.i will take the solution above with P(D)=...=0,325