Help with highly quant interview questions
Hi,
I would like to ask two possible interview questions, any help would mean a lot to me, please try to explain answers, if possible.
1.) You are waiting for a bus which it takes a round trip of 10 minutes to complete (starts again when it completes one tour). There is an ice cream shop somewhere on the bus route. The bus driver flips a fair coin every time it passes by it and if "H", spends 10 minutes to eat ice cream and then continue the tour. What is your expected waiting time ? What is the coin is biased?
2.) There's a rounded table, you wanna place three legs randomly, what's the chance the table stands?
Thank you very much for your answers.
2 is impossible to answer as phrased. The question you might be thinking of is you have 3 legs of a table equally placed around the perimeter of the circle.
I don't think that 2 is impossible as written.
Assuming the legs are sturdy (i.e. will not break under the weight of the table) and very thin relative to the area of the circle, any random attachment to the underside will form a triangle w.p. 1. The table will stand upright if the center of mass of the table is contained inside this triangle. Otherwise, it will tip over.
Assuming the weight of the surface is equally distributed, the center of mass is at the center of the circle.
So it's asking, if we pick 3 random points inside a circle, what's the probability they will form a triangle containing the center of the circle?
Missing point which of those questions are highly quant, but
1) It takes bus 20 minutes on average to complete the round trip (10 mins + 2 x 50% probability of taking a 10 minute break). This value will be uniformly distributed, so the expected waiting time is 10 minutes. If the coin is biased to show more heads, this time will increase.
2) Scroll down for an explanation, http://www.glassdoor.com/Interview/Given-a-round-table-randomly-place-t… Basically,
1) Is it not like this: 0,5 probability for trip to take 10 min + 0,5 probability for a 20min trip = 5 + 10 = 15 min expected time?
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