probability Help.?

Question

adventurer dakota davis is carefully walking across an ancient 120 foot long rope bridge that is stretched across a canyon whose walls rise 90 feet above a river. If the rope breaks where he is holding it (a random point), what is the probability that one end of the rope will hit the piranha-infested waters below?

please explain.

Answer 1

Hi,

The probability is 50% that one end of the rope will hit the piranha-infested waters below. That's because it is 90 feet down the cliff to the river, so if he is in the first 30 feet and the rope breaks, one piece will be less than 30 feet long but the other will be more than 90 feet long. If he was in the middle 60 feet of the bridge both pieces will be more than 30 feet and less than 90 feet. During the final 30 feet, the problem reverses and goes back to one piece being less than 30 feet and one piece more than 90 feet.

So he is in danger the first 30 feet and the last 30 feet where one piece of rope is always less than 30 feet long and the other is more than 90 feet long. That's a total of 60 out of the 120 feet across the bridge for a 50% probability.

I hope that helps!! :-)

Answer 2

120 - 90 = 30
For the first 30 feet and the last 30 feet the end of the rope can reach the water, so
P(L=90) = (30 + 30)/120 = 0.5

Answer 3

i think its asking if u cut that rope at any point what is the probability that one end will be 90 feet long

Answer 4

120=30+90
120=90+30
both sides.
2X30 /90 (total)=p
.
p=60/90=6/9=2/3=0.666_
p=~67%