fun math puzzles
Author
This is not homework; I am an expert in Probability.
I.
Use this diagram:
A B C D
A'' B'' C'' D'' E'' F''
A-F'' are all trivial points.
1. If you randomely select 3 points from the whole group [of 10 points], what is the probability of forming a triangle with 2 points from the bottom and 1 point from the top?
2. What''s the probability of not making a triangle with your point selection of 3?
(skill level: medium)
II.
No diagram for this one:
In an orthogonal 8x7-square grid, how many rectangles can be formed? Need a hint? Here: remember that a rectangle can be formed by two of the horizontal lines in the grid and two vertical lines in the grid. And don''t forget that a square is a rectangle. 8 squares by 7 squares equals 56 squares in the grid.
(difficulty: hard)
If you can answer one of the above problems, then you can contribute one of your own. I''ll be posting the answer in 30 minutes from the live time of this post.
II: 588 rectangles.
...now for I...
edit: oh, I thought you meant 8x7 points... for 8x7 squares, the answer is 1008. And that's assuming that all rectangles have sides parallel to the rows & columns... there are other ones besides those ones.
[edited by - vanillacoke on May 12, 2003 10:44:04 PM]
...now for I...
edit: oh, I thought you meant 8x7 points... for 8x7 squares, the answer is 1008. And that's assuming that all rectangles have sides parallel to the rows & columns... there are other ones besides those ones.
[edited by - vanillacoke on May 12, 2003 10:44:04 PM]
I.
1. 1/6 is probablity of getting thing you said.
2. 1/5 is probability of getting no triangle.
edit: that's assuming that the points are picked without replacement.
[edited by - vanillacoke on May 12, 2003 10:48:41 PM]
1. 1/6 is probablity of getting thing you said.
2. 1/5 is probability of getting no triangle.
edit: that's assuming that the points are picked without replacement.
[edited by - vanillacoke on May 12, 2003 10:48:41 PM]
Author
Your first answer was correct: 588. If you disagree, wait''ll I post the solutions in 15 mins.
Author
Re to your second post: 1/6 is incorrect. The probability is actually (for number 1) a 50% chance of forming a square out of 2 bottom and 1 top in a selection of 3 from the group of 10. Again, wait for my answer post.
Author
Twelve minutes and counting...
When are you going to try''n stump me? I said you could contribute if you got one right, and you did. Now it''s my turn to have fun!
When are you going to try''n stump me? I said you could contribute if you got one right, and you did. Now it''s my turn to have fun!
It''s not mine but I love this one:
A game show contestant is presented with three doors numbered 1, 2, and 3. Behind one of the doors is the grand prize. The contestant chooses a door. The host, who knows what''s behind each door, opens up one of the two remaining doors which doesn''t have the grand prize behind it. He then asks the contestant, "Do you want to stay with your original choice or would you like to switch to the other remaining door?"
Should the contestant stay with her original choice, should she change to the other door, or does it not make any difference?
A game show contestant is presented with three doors numbered 1, 2, and 3. Behind one of the doors is the grand prize. The contestant chooses a door. The host, who knows what''s behind each door, opens up one of the two remaining doors which doesn''t have the grand prize behind it. He then asks the contestant, "Do you want to stay with your original choice or would you like to switch to the other remaining door?"
Should the contestant stay with her original choice, should she change to the other door, or does it not make any difference?
Ok. You have a regular hexagon, in the cartesian plane. The y-coordinates of the vertices are unique elements of the set {0,2,4,6,8,10}. Find the area of the hexagon.
Author
The odds of the grand prize being in one of the two unopened doors is 50:50, thus it does not matter which door she chooses.
This topic is closed to new replies.
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