In a stall game, the whole surface of a table is covered by square tiles of side 6cm as shown. A participant is asked to throw a metal disc of diameter 4cm onto the table. If the disc does not touch the side of any square, he wins. If it touches a side, he loses. Suppose a participant throws the disc and it stays on the table, what is the probability that he wins the game?
THZ!!
Probability Problem
2008-05-27 12:15 am
回答 (2)
2008-05-27 12:30 am
✔ 最佳答案
The answer is one-ninth.First place the disc to the corner just touching the two sides of the tiles. Move the disc along the edges round the tile and all the areas within this space is the possible area of winning.
This area actually form a square of 2x2 cm from the center of the tile.
So probablility of winning is 2x2 / 6x6 which is one-ninth.
Hope this helps.
2008-05-27 12:20 am
P (win)
= P (the disc does not touch the side of any square)
= area of circle/ area of square
= pi/9
2008-05-26 16:24:19 補充：
it's about 0.34906585033
= P (the disc does not touch the side of any square)
= area of circle/ area of square
= pi/9
2008-05-26 16:24:19 補充：
it's about 0.34906585033
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