F3 probability

Crystal

2011-01-03 12:55 am

1.The following is a game in an amusement park
A participant needs to throw a token with the diameter of 2cm onto the table,of which the table top is divided into indentical 3cm x 3cm squares by lines drawn on it.A price is given if the token thrown does not touch the lines on the table.

(a) If the token does not touch any side of a square,what is the area if the region formed by the possible locations of the centre of the token? (ans=1cm22 )
(b) Find the probability of winning a prize by throwing a token.(ans=1/9)

圖片參考：http://imgcld.yimg.com/8/n/HA04937267/o/701101020090413873435400.jpg

2.The figure shows a circular track with O as its centre,and there are 2marbles rolling along the track randomly.A prize will be given if the angle at the centre formed by these two marbles with O is less than or equal to 60 degree when they stop rolling.Find the probability of winning a prize.(ans=1/3)

圖片參考：http://imgcld.yimg.com/8/n/HA04937267/o/701101020090413873435411.jpg

想要2題既step同解釋

更新1:

第1題我唔明= = 有無圖upload黎睇下..?thx

回答 (1)

myisland8132

2011-01-03 1:17 am

✔ 最佳答案

(a) Let the coordinate of the centre of the square (0,0) and place the centre of the token on it. Then it is obviously that the maximum distance along any direction (east, west, south or north) of the "centre of the token" such that the token does not touch any side of a square is is 1 cm only.

So, the area is 1 cm * 1cm =1 cm^2

(b) P
=Area obtained in part (a)/ The area of square
=1/(3*3)
=1/9

2 Since the largest subtended angle between two marbles is 60 degrees and there are two possible choices for their relative location. i.e Red one is on the right of Green one or vice versa. So, the total allowed range is 120 degrees. The probability of winning a prize = 120/360 = 1/3

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