Today Puzzle #697
Storm Dennis saw a ghost ship wash up on the Irish Coast which had been drifting for more than a year. If a ship is in the middle of an ocean and travels 50 miles each day, either East or West depending on a random wind which can change just daily, what is the probability it will be more than 1000miles from its point of origin after 400 days?
Today’s #PuzzleForToday has been set by Dr Shaun Fitzgerald, Fellow of Girton College
Click here for the answer
The standard deviation S of a one dimensional random walk with number N time steps and where D is the distance travelled in each time step is given by D x sqrt (N), in the case where N is very large. Applying the formula we have S = 50 x sqrt(400) = 50 x 20 = 1,000 miles. The distance in question is therefore 1 standard deviation from the point of origin. Given a normal distribution, the probability of the ship being beyond that distance after 400 days is 100%-68% = 32%, i.e. about 30% in this case (noting that the formula is only strictly applicable in the case of large N).
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