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1.Four people need to cross a rickety rope bridge to get back to their
camp at night. Unfortunately, they only have one flashlight and it only
has enough light left for seventeen minutes. The bridge is too
dangerous to cross without a flashlight, and it’s only strong enough to
support two people at any given time. Each of the campers walks at a
different speed. One can cross the bridge in 1 minute, another in 2
minutes, the third in 5 minutes, and the slow poke takes 10 minutes to
cross. How do the campers make it across in 17 minutes? Lets call the guys 1,2,5,10 for convenience based on time required to go. First, 1 and 2 go, 1 comes back , Total Time: 2+1 = 3 Second, 5 & 10 go, 2 comes back (remember 2 is on other side from prev round) , Total Time = 10+ 2+ 3(prev round) = 15. Third, 1 and 2 remain ,they go, Total time = 2 + 15(from prev round) = 17. 2. If the probability of observing a car in 30 minutes on a highway is 0.95, what is the probability of observing a car in 10 minutes (assuming constant default probability)? solution 1: You have to look at your probability of NOT seeing a car, which is .05 in 30 minutes. In order to break this down into 10 minute chunks, you need to figure out how you arrived at that probability, which would be x * x * x = .05, so x ^ 3 = .05. I don‘t have a calculator, but the then you would have the third root of .05. Then you would subtract that from 1 and arrive at your 10 minute probability. solution 2: Let p is a probability to see a car in 10 minutes. Then (1-p) is probability NOT to see a car in 10 minutes. Then probability NOT to see a car in 30 minutes is (1-p)*(1-p)*(1-p). (1-p)^3 == 0.05 So p = 1-0.05^(1/3)~ 0.63 3.In a country in which people only want boys, every family continues to have children until they have a boy. if they have a girl, they have another child. if they have a boy, they stop. what is the proportion of boys to girls in the country? 4. You have an empty room, and a group of people waiting outside the room. At each step, you may either get one person into the room, or get one out. Can you make subsequent steps, so that every possible combination of people is achieved exactly once? |
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