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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: yabbaboo on May 20, 2010, 08:59:58 pm

Title: Need a quick help on probability!
Post by: yabbaboo on May 20, 2010, 08:59:58 pm: A square board with side length 10 cm is placed on a table. A game consists of throwing a disc of radius 4cm onto the table, and a pint is scored if the disc lies completely within the board (touching an edge is acceptable). If a player always gets the centre of the disc into the board, what is the probability of scoring a point?

I am not sure how to work this out. The answer is 9/25 by the way. Can you show me how?
Title: Re: Need a quick help on probability!
Post by: the.watchman on May 20, 2010, 09:06:24 pm: Looking at the board, it is obvious that, for the point to be scored, the centre of the disc must land at least 4cm from the nearest edge.
Therefore, the dimensions of the area of the board which the centre can land in is 2x2 (take off four from each side)

SO the probability = $\frac{2\cdot 2}{10 \cdot 10} = \frac{1}{25}$

I think the DIAMETER of the disc needs to be 4cm for the 9/25 to be right :P
Then the 'success' area is 6x6
And the probability = $\frac{6\cdot 6}{10 \cdot 10} = \frac{9}{25}$