A coin of radius 1 cm is tossed onto a plane surface that has been tesselated by rectangles whose measurements are all 8cm by 15cm. What is the probability that the coin lands within one of the rectangles?

My answer is 0.65

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- Jun 9th 2011, 09:38 PMVeronica1999Coin tosed onto tessalated surface.
A coin of radius 1 cm is tossed onto a plane surface that has been tesselated by rectangles whose measurements are all 8cm by 15cm. What is the probability that the coin lands within one of the rectangles?

My answer is 0.65 - Jun 9th 2011, 10:20 PMSoroban
Hello, Veronica1999!

Quote:

A coin of radius 1 cm is tossed onto a plane surface that has been tesselated

by rectangles whose measurements are all 8cm by 15cm.

What is the probability that the coin lands within one of the rectangles?

My answer is 0.65

*Correct!*

- Jun 9th 2011, 10:56 PMsean.1986
For anyone wondering how Veronica came to this answer, the centre of the coin has to be at least 1cm from the edge of the rectangle it falls into, for the whole coin to be inside it. So if you draw a rectangle inside the original one, whose sides are a distance of 1cm from the original rectangle, you end up with a 6cm by 13cm rectangle inside.

The inner rectangle has an area of 6*13 = 78 cm^2.

The outer has an area of 8*15 = 120 cm^2.

The probability of the coin's centre landing within the inner rectangle and hence the whole coin landing within the outer one, is 78/120 = 0.65.