Do we use conditional probability formula here

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Npkaranth

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A possum needs to cross a track to get from tree to waterhole. It’s a single railway track with 2.0 trains/hour. The trains are all 100 meters long and travel at 60 km/ hr. it takes her 5 sec to cross the track . What is the probability that she makes it safely if she starts at random time
 
Npkaranth said:
A possum needs to cross a track to get from tree to waterhole. It’s a single railway track with 2.0 trains/hour. The trains are all 100 meters long and travel at 60 km/ hr. it takes her 5 sec to cross the track . What is the probability that she makes it safely if she starts at random time
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What do you think? Please share your work/thoughts about this problem!
 
Frankly speaking , I have no insight as such. I am doctor mom trying to help my kid but what I understood is the probability of possum being safe is conditional on a train not passing at the time of crossing
 
How many seconds are there in an hour? During how many of these seconds would it be safe for the possum to START walking across the track?
 
Npkaranth said:
A possum needs to cross a track to get from tree to waterhole. It’s a single railway track with 2.0 trains/hour. The trains are all 100 meters long and travel at 60 km/ hr. it takes her 5 sec to cross the track . What is the probability that she makes it safely if she starts at random time
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In any given hour, how much time will there be a train on the tracks? That is the key to solving this problem.
 
Npkaranth said:
ya the possum would be unsafe for 2 min in an hour
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Please show your working out so that we know where you're going wrong. It doesn't seem like you used the 100m distance when you worked out 2min. Part of the required work is to calculate how much time it takes one train to travel 100m. This is the same as the length of time that (the whole length of) the train will take to run over any one spot on the track.

Above I suggested using seconds as the unit of time because that will make it slightly easier when you take into account the speed of the possum! But if you prefer then it's fine to work with minutes as your unit of time.
 
Npkaranth said:
the question was typed wrong. its 20 trains/hr not 2.0
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Your post took a while to be approved (since it was one of your first 5 posts), therefore the helpers didn't see it.

Npkaranth said:
20 trains =100X 20=2000m=2km so 2min
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You didn't show how you "turned" 2km into 2min, but yes, 2min is the total time that train(s) will be on any single point of that track during an hour :)

Have you got any ideas how to use this part the question, "it takes her 5 sec <for the possum> to cross the track"?
 
Npkaranth said:
I was thinking that 5 sec before every train should also be unsafe
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Exactly 5 seconds before every train would be unsafe? So 4 seconds before the train arrives the possum can start to cross the tracks and be safe?
 
...and therefore how much extra unsafe time is there per hour (due to the possum's slow speed)?

Then you can use your response#10, in combination with the answer above, to find the total unsafe time per hour?
 
Cubist said:
...and therefore how much extra unsafe time is there per hour (due to the possum's slow speed)?

Then you can use your response#10, in combination with the answer above, to find the total unsafe time per hour?
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Total unsafe would be 2 min 100 sec . so does it come to 93.88% possum will cross safely
 
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