Maths probability

When the coin in thrown into the box, the centre of the coin must lie in the shaded square:

Area of the shaded square

= (10 - 1 x 2)2 cm2

= 64 cm2


When the coin lie entirely in the shaded area, the centre of the coin must lie in a smaller square with side (8 - 1 x 2) cm = 6 cm

Area of the smaller square

= 62 cm2

= 36 cm2


Probability

= (36 cm2)/(64 cm2)

= 9/16
=

Uncle Michael 是對的。

這作法假設了 coin 掉進 box 內，一定是平放，不為斜站在邊上。所以 center of coin 一定會落入 shaded area。至於要整個 coin 落入 shaded area, 就要 center of coin 落入 6x6 的 centered square 內。所求機率為 36/64 = 9/16.

the area of shaded area:
(10-1-1)^2=64cm^2

the area of the coin:
πr^2=(3.14)(1)^2=3.14cm^2

P(the coin lies entirely in the shaded area):
64/3.14=20.38%

64%
the probability that it will lie entirely in the box:
10*10/10*10=100%
the probability that it will lie entirely in theshaded area:
(10-2)*(10-2)/10*10=8*8/10*10
=64%