A MC Question

👨🏻‍🏫 學術台數學

用戶85377

2009-04-26 8:05 am

Explain it clearly.

1. In the figure, a grid consists of 25 identical squares in which two are shaded. If one of the white squares is chosen random and shaded, find the probability that the grid has only one axis of symmetry.

更新1:

I cannot pose the figure. Sorry@

更新2:

I try to draw the diagram S: means shaded square W: means white square W W W W S W W W W W W W S W W W W W W W W W W W W

更新3:

The answer is 4/23. I think you know how to do this question and I do not how c omes the number "23".

回答 (2)

Steve

2009-05-01 9:52 pm

✔ 最佳答案

in your figure, if only one axis of symmetry,
it should be look like the following-:

W W W W S
W W W W W
W W S W W
W W W W W
W W W W S
or
S W W W S
W W W W W
W W S W W
W W W W W
W W W W W

that means , the probability is 2/23

2009-05-06 22:21:33 補充：
我稔我同另一位朋友都搞錯左少少野, 答案應該係咁:
1.
W W W W S
W W W W W
W W S W W
W W W W W
W W W W S
2.
S W W W S
W W W W W
W W S W W
W W W W W
W W W W W
3.
W W W W S
W W WS W
W W S W W
W W W W W
W W W W W
4.
W W W W S
W W W W W
W W S W W
W S W W W
W W W W W

2009-05-06 22:21:37 補充：
qa245we的第3個錯左, 因為有多過一個對稱軸, 以上的第4個組合方法才對, 本來個figure係25格, 扣除已經shade左的2格以外剩下的23格去再shade多一格, 所以答案係4/23, sorry for the previous mistake

參考: , me, me

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Chun Hin

2009-05-07 5:33 am

I know how the 23 is come from.
There are 2 shaded squares,
so Total square - Shaded squares = unshaded squares

25-2=23
The shaded square may be in

1. S W W W S
W W W W W
W W S W W
W W W W W
W W W W W

2. W W W W S
W W W W W
W W S W W
W W W W W
W W W W S

3. W W W W S
W W W W W
W W S W W
W W W W W
S W W W W

4. W W W W S
W W W S W
W W S W W
W W W W W
W W W W W

Therefore, the probability =4/23

2009-05-07 22:45:22 補充：
I think stevekam80's answer is correct and sorry for my mistakes

2009-05-07 22:46:44 補充：
The third answer should be:

3. W W W W S
W W W W W
W W S W W
W S W W W
W W W W W

2009-05-07 22:46:58 補充：
Hope I can help you.

參考: myself

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