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Today Puzzle #671

Puzzle No. 671 – Friday 7 February 2020

Robin Hood is showing off his skills. He shoots an arrow North, trying for the Sherwood Forest distance record. This arrow has a rubber head and bounces up to two times. Each time it bounces, it goes off in a random direction (North, South, East or West). The current distance record is set at 99m North of Robin. If Robin’s first shot goes 70m, the first rebound 50m and the second rebound 30m, what is the chance the Arrow will finish further North than the record? What is the chance the arrow will end up behind Robin?

Today’s #PuzzleForToday has been set by Dr James Hind, is a Lecturer in Statistics in the School of Science and Technology at Nottingham Trent University

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A1 To break the record, Robin needs either of the bounces to go North, and none of the bounces to go South. The chance of this is 31.25%. The only way the arrow could end up behind him is if both bounces move the arrow South, the chance of this is just 6.25%. You can find these answers using a probability tree, counting how far North the arrow travels in every case:

First shot First rebound Second rebound Record winner? Behind Robin? 70 N=120 N=150 y 0 E=120 y 0 W=120 y 0 S=90 0 0 E=70 N=100 y 0 E=70 0 0 W=70 0 0 S=40 0 0 W=70 N=100 y 0 E=70 0 0 W=70 0 0 S=40 0 0 S=20 N=50 0 0 E=20 0 0 W=20 0 0 S=-10 0 1 (5/16) (1/16) 0.3125 0.0625

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