There is a game in an amusement playground. The surface of a square table
is divided into 25 3cmX3cm squares. A coin with a diameter of 2 cm is
thrown on the table by a player. The player will win a prize if the coin does
not touch any lines on the table.
a)Aussume that a coin falls on to one of the 3cmX3cm squares ABCD. If it
does not touch the side of AB, what is the minimum distance between the
centre of the coin and AB?
b)If the coin does not touch the sides of ABCD, what is the maximum area
onto which the centre of the coin can fall?
c)Find the probability of wining a prize in each throw.
p.s. Please write full steps. Thank you. This help me to understand.
中三數學不明白~ 機率（請別介意本人打英文）
2008-03-20 12:17 pm
回答 (4)
2008-03-20 2:12 pm
✔ 最佳答案
a) As the coin does not touch the side of AB and for the centre of coin is closest to AB, the coin is nearly touching AB.minimum distance = radius of coin = 1cm
b) As from above, the coin can only occupy a sqaure of sides 1 cm shorter than ABCD. ie
the coin's square is (3-1)x(3-1) = 4 cm2
c) assume:
1) the width of line is negligible to the dimension of the table.
2) coin will fall off the table if the centre of coin is not at table and such occasions are not considered.
3) the throw is not baised in anyway, ie would not try to aim at the centre of squares.
P(winning) = ratio of area = 2x2 / 3x3 = 4/9
2008-03-21 12:52 am
A. 1.0 CM -- the radius of the coin
B. (3 - 1) X (3 -1) = 4
C. ((2x2)*25) / ((3x3)*25) = 4 / 9 the ratio of the area. It is because the table has 25 squares and each one is independent from each other.
The previous answer and the modification
B. (3 - 1) X (3 -1) = 4
C. ((2x2)*25) / ((3x3)*25) = 4 / 9 the ratio of the area. It is because the table has 25 squares and each one is independent from each other.
The previous answer and the modification
2008-03-20 10:26 pm
Assume that the width of lines is negligible.
a) The minimum distance between the centre of the coin and the side AB is
the radius of the coin = diameter/2 = 2/2 = 1 cm
b) According to a), the centre of the coin cannot fall within 1 cm to any side of ABCD. The maximum area onto which the centre of the coin can fall is
(3-1-1)(3-1-1) = 1*1 = 1 cm^2
c) Assume that the centre of the coin will always fall on the table and no fall off occasion will be considered. Therefore, the probability of wining a prize in each throw = area of the coin not touching any sides / area of the table
= 1*25/3*3*25
= 1/9
2) coin will fall off the table if the centre of coin is not at table and such occasions are not considered.
a) The minimum distance between the centre of the coin and the side AB is
the radius of the coin = diameter/2 = 2/2 = 1 cm
b) According to a), the centre of the coin cannot fall within 1 cm to any side of ABCD. The maximum area onto which the centre of the coin can fall is
(3-1-1)(3-1-1) = 1*1 = 1 cm^2
c) Assume that the centre of the coin will always fall on the table and no fall off occasion will be considered. Therefore, the probability of wining a prize in each throw = area of the coin not touching any sides / area of the table
= 1*25/3*3*25
= 1/9
2) coin will fall off the table if the centre of coin is not at table and such occasions are not considered.
2008-03-20 6:56 pm
a) As the coin does not touch the side of AB and for the centre of coin is closest to AB, the coin is nearly touching AB.
minimum distance = radius of coin = 1cm
b) As from above, the coin can only occupy a sqaure of sides 1+1 cm shorter than ABCD. ie
the coin's square is (3-2)x(3-2) = 1 cm2
c) assume:
1) the width of line is negligible to the dimension of the table.
2) coin will fall off the table if the centre of coin is not at table and such occasions are not considered.
3) the throw is not baised in anyway, ie would not try to aim at the centre of squares.
P(winning) = ratio of area = 1x1 / 3x3 = 1/9
minimum distance = radius of coin = 1cm
b) As from above, the coin can only occupy a sqaure of sides 1+1 cm shorter than ABCD. ie
the coin's square is (3-2)x(3-2) = 1 cm2
c) assume:
1) the width of line is negligible to the dimension of the table.
2) coin will fall off the table if the centre of coin is not at table and such occasions are not considered.
3) the throw is not baised in anyway, ie would not try to aim at the centre of squares.
P(winning) = ratio of area = 1x1 / 3x3 = 1/9
收錄日期: 2021-04-23 22:49:02
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