a) Imagine a rope stretching around the equator of a symmetrical spherical earth and touching the surface at all points. How much longer would the rope have to be such that it is now raised exactly one metre above the earth's surface at all points?
If D is the diameter of the Earth (in meters) than the rope will have to be PiD to add a meter the rope will be Pi(D+2) = PiD+2Pi so the extra length is 2Pi metres.
a) Imagine a rope stretching around the equator of a symmetrical spherical earth and touching the surface at all points. How much longer would the rope have to be such that it is now raised exactly one metre above the earth's surface at all points?
Pi x 41 : - )
Units, please, Irving? Units?
See me in my study after prep (whatever that is).
Err, sorry sir Pi x (Diameter of earth + 2m) i think?????? as you've increased the diameter by a metre either side so to speak.
I have used brackets to please all the BODMAS lovers out there.
There are 4 marbles in a bag. One is red, one is yellow and the other two are blue. If I pick out two marbles at random, look in my hand and show you a blue marble, what are the odds that the other marble is also blue?
Just over 28% chance that the other marble is blue.
Having thought about this again, it doesn't matter if he shows you one of the marbles or not.
The chances of scooping 2 blues in a single dip into the bag is 1 in 6, and this is not altered by the fact that you are shown the colour of one afterwards.
I would say the chances of scooping two blues in a single swoop is 1 in 4. (R & B, Y & B, R & Y, B & . If after you have scooped two balls and show 1 and it is blue the chance of the second one being blue is 1 in 3.
There are 4 marbles in a bag. One is red, one is yellow and the other two are blue. If I pick out two marbles at random, look in my hand and show you a blue marble, what are the odds that the other marble is also blue?
Just over 28% chance that the other marble is blue.
Having thought about this again, it doesn't matter if he shows you one of the marbles or not.
The chances of scooping 2 blues in a single dip into the bag is 1 in 6, and this is not altered by the fact that you are shown the colour of one afterwards.
I would say the chances of scooping two blues in a single swoop is 1 in 4. (R & B, Y & B, R & Y, B & . If after you have scooped two balls and show 1 and it is blue the chance of the second one being blue is 1 in 3.
There are 4 marbles in a bag. One is red, one is yellow and the other two are blue. If I pick out two marbles at random, look in my hand and show you a blue marble, what are the odds that the other marble is also blue?
Just over 28% chance that the other marble is blue.
Having thought about this again, it doesn't matter if he shows you one of the marbles or not.
The chances of scooping 2 blues in a single dip into the bag is 1 in 6, and this is not altered by the fact that you are shown the colour of one afterwards.
I would say the chances of scooping two blues in a single swoop is 1 in 4. (R & B, Y & B, R & Y, B & . If after you have scooped two balls and show 1 and it is blue the chance of the second one being blue is 1 in 3.
I prefer 1 in 5.
When you remove two balls at random, there are six possible combinations (R+Y, R+B1, R+B2, Y+B1, Y+B2, B1+B2). On revealing the fact that one of the balls removed is blue, you eliminate the R+Y possibility, hence any of the remaining five combinations is possible, giving a 20% chance of each.
There are 4 marbles in a bag. One is red, one is yellow and the other two are blue. If I pick out two marbles at random, look in my hand and show you a blue marble, what are the odds that the other marble is also blue?
Just over 28% chance that the other marble is blue.
Having thought about this again, it doesn't matter if he shows you one of the marbles or not.
The chances of scooping 2 blues in a single dip into the bag is 1 in 6, and this is not altered by the fact that you are shown the colour of one afterwards.
I would say the chances of scooping two blues in a single swoop is 1 in 4. (R & B, Y & B, R & Y, B & . If after you have scooped two balls and show 1 and it is blue the chance of the second one being blue is 1 in 3.
I prefer 1 in 5.
When you remove two balls at random, there are six possible combinations (R+Y, R+B1, R+B2, Y+B1, Y+B2, B1+B2). On revealing the fact that one of the balls removed is blue, you eliminate the R+Y possibility, hence any of the remaining five combinations is possible, giving a 20% chance of each.
R+ B1 is the same as R+ B2 (as far as the puzzle is concerned) so these are the same combination. Similarly, Y+B1 and Y+B2 are one combination not 2.
There are 4 marbles in a bag. One is red, one is yellow and the other two are blue. If I pick out two marbles at random, look in my hand and show you a blue marble, what are the odds that the other marble is also blue?
Just over 28% chance that the other marble is blue.
Having thought about this again, it doesn't matter if he shows you one of the marbles or not.
The chances of scooping 2 blues in a single dip into the bag is 1 in 6, and this is not altered by the fact that you are shown the colour of one afterwards.
I would say the chances of scooping two blues in a single swoop is 1 in 4. (R & B, Y & B, R & Y, B & . If after you have scooped two balls and show 1 and it is blue the chance of the second one being blue is 1 in 3.
I prefer 1 in 5.
When you remove two balls at random, there are six possible combinations (R+Y, R+B1, R+B2, Y+B1, Y+B2, B1+B2). On revealing the fact that one of the balls removed is blue, you eliminate the R+Y possibility, hence any of the remaining five combinations is possible, giving a 20% chance of each.
R+ B1 is the same as R+ B2 (as far as the puzzle is concerned) so these are the same combination. Similarly, Y+B1 and Y+B2 are one combination not 2.
I disagree. Imagine if one of the blue balls had a tiny white dot on it. Do you still make R+B1 and R+B2 the same?
As we know, the original length of the rope is somewhere in the region of 40 million metres. So, you are telling me that, by extending it by just over six metres (2pi) to around 40,000,006 metres, the entire rope will now be raised to a height of one metre above the surface of the earth?
*checks around the class for smirking from school chums*
OK, now try with 100 blue balls. Do you still make R+B1, R+B2 ... R+B100 equal to the same single combination?
Yes. In that sistuation there would be 102 balls in the bag. There would still be only the same possible 4 combinations. But now the chances of picking 2 blues in one swoop are 100 in 102. If you show the first ball and it is Blue the chances of the second one being Blue is 99 in 101.
As we know, the original length of the rope is somewhere in the region of 40 million metres. So, you are telling me that, by extending it by just over six metres (2pi) to around 40,000,006 metres, the entire rope will now be raised to a height of one metre above the surface of the earth?
*checks around the class for smirking from school chums*
I am. I think it would be the same length if you were to wrap a string around a ping pong ball.
As we know, the original length of the rope is somewhere in the region of 40 million metres. So, you are telling me that, by extending it by just over six metres (2pi) to around 40,000,006 metres, the entire rope will now be raised to a height of one metre above the surface of the earth?
*checks around the class for smirking from school chums*
I am. I think it would be the same length if you were to wrap a string around a ping pong ball.
Excellent, FOD! I like your style. You are indeed correct ... although the result is somewhat surprising, don't you think?
Irving ... you would do well to take a leaf out of FOD's book. You don't see him with his nose stuck in some popular culture magazine.
For the marbles puzzle, it is 1 in 5. Quite simply, there are six combinations that can be drawn, AB, AC, AD, BC, BD or CD. If A and B are the blue ones, say, there are 5 combinations where there is at least 1 blue marble. Therefore, if a blue on is shown, it is a 1 in 5 chance that the other is blue as AB is the only combination of the 5 combinations where a blue is present.
Taking the diameter of the earth at 12,756km (Google) add 000 to make metres then adding two (one metre either side of the earth on the diameter) we get figures of 40074155.8 before raising the rope and 40074162.1 after raising it. So it would be 7 metres longer. Your faithfully, Mr A Nal.
Taking the diameter of the earth at 12,756km (Google) add 000 to make metres then adding two (one metre either side of the earth on the diameter) we get figures of 40074155.8 before raising the rope and 40074162.1 after raising it. So it would be 7 metres longer. Your faithfully, Mr A Nal.
it wouldn't be, 1 meter all the way around not in just 2 places.
The diameter is only lengthened by two metres (one at each end) the circumference of that diameter increases by 6.3metres (rounded up to 7) in my calculations.
The diameter is only lengthened by two metres (one at each end) the circumference of that diameter increases by 6.3metres (rounded up to 7) in my calculations.
Nur nur de nur nur :-)
Impressive that you two wrestle with this long after your chums have arrived at the correct answer, long after the exam has finished, long after the exam room has been darkened and closed for the night, long after the school has been pulled down and converted into a retail park.
Now, who's first up to tell me what's wrong with the faster runner/slower runner scenario?
Comments
I have used brackets to please all the BODMAS lovers out there.
I prefer 1 in 5.
When you remove two balls at random, there are six possible combinations (R+Y, R+B1, R+B2, Y+B1, Y+B2, B1+B2). On revealing the fact that one of the balls removed is blue, you eliminate the R+Y possibility, hence any of the remaining five combinations is possible, giving a 20% chance of each.
R+ B1 is the same as R+ B2 (as far as the puzzle is concerned) so these are the same combination. Similarly, Y+B1 and Y+B2 are one combination not 2.
Yes, as far as the puzzle is concerned.
OK, so let me check, FOD ...
As we know, the original length of the rope is somewhere in the region of 40 million metres. So, you are telling me that, by extending it by just over six metres (2pi) to around 40,000,006 metres, the entire rope will now be raised to a height of one metre above the surface of the earth?
*checks around the class for smirking from school chums*
I'm still waiting.......
How far did the dog run into the woods?
Half of the way - Final Answer!
Excellent, FOD! I like your style. You are indeed correct ... although the result is somewhat surprising, don't you think?
Irving ... you would do well to take a leaf out of FOD's book. You don't see him with his nose stuck in some popular culture magazine.
Admirable qualities, FOD.
There may be a place available at the prefect table in the near future. I'll keep you in mind.
How do snow plough drivers get to work in the morning?
Your faithfully,
Mr A Nal.
Nur nur de nur nur :-)
Impressive that you two wrestle with this long after your chums have arrived at the correct answer, long after the exam has finished, long after the exam room has been darkened and closed for the night, long after the school has been pulled down and converted into a retail park.
Now, who's first up to tell me what's wrong with the faster runner/slower runner scenario?