# How is probability being used in this case?

## 17 posts in this topic

I am confused about the use of probability in this example:

"Last Thursday, Dec. 23, scientists announced that a space rock named 2004 MN4 had about a 1-in-300 chance of striking Earth on April 13, 2029"

I can understand the statement, "There's a 50% chance that a coin toss will be heads or tails." because this refers to a repeatable event. In other words, whenever you encounter a coin toss, you have a probability that will tell you the likely outcomes.

What does the 1 in 300 mean? This is not a repeatable event. It is a fairly unique situtation, so how can scientists say "a 1 in 300 chance"? And what does it mean?

Metaphysically the asteroid is the same as the coin. There's a 100% chance of the entities involved following their nature. We assign probability because we don't measure everthing. But for some reason I don't get how they come up with such numbers. Does this mean they polled 300 scientists? Or did they use 300 computer models with different error margins?

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I am confused about the use of probability in this example:

"Last Thursday, Dec. 23, scientists announced that a space rock named 2004 MN4 had about a 1-in-300 chance of striking Earth on April 13, 2029"

...

What does the 1 in 300 mean? This is not a repeatable event. It is a fairly unique situtation, so how can scientists say "a 1 in 300 chance"? And what does it mean?

Metaphysically the asteroid is the same as the coin. There's a 100% chance of the entities involved following their nature. We assign probability because we don't measure everthing. But for some reason I don't get how they come up with such numbers. Does this mean they polled 300 scientists? Or did they use 300 computer models with different error margins?

The 1 in 300 ratio is a more convenient way to represent the approximate probability of 0.33% in the context of an article in a popular publication or website. They mean exactly the same thing. The method used to calculate the probability has nothing to do with the way it is expressed.

Personally, if a probability is less than 1%, I like it expressed as a ratio; if it is greater than 1%, I like to see it as a percentage.

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I am confused about the use of probability in this example:

"Last Thursday, Dec. 23, scientists announced that a space rock named 2004 MN4 had about a 1-in-300 chance of striking Earth on April 13, 2029"

I can understand the statement, "There's a 50% chance that a coin toss will be heads or tails." because this refers to a repeatable event. In other words, whenever you encounter a coin toss, you have a probability that will tell you the likely outcomes.

What does the 1 in 300 mean? This is not a repeatable event. It is a fairly unique situtation, so how can scientists say "a 1 in 300 chance"? And what does it mean?

Probability is an epistemological concept, not a metaphysical one. It is an expression of the state of our knowledge about an event. Metaphysically, either the space rock will crash into Earth, or it will not. If we had perfect knowledge of all the factors involved, then we would have no need for probability in regard to the space rock; we would know.

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The 1 in 300 ratio is a more convenient way to represent the approximate probability of 0.33% in the context of an article in a popular publication or website. They mean exactly the same thing.

Thank you for explaining how the percentages work.

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Thank you for explaining how the percentages work.

Without knowing the specifics involved, there could be other factors used in measuring the percentage. For example, given various sizes and compositions of rocks, if 300 rocks have intersected the earth's orbit in the past, then 1 may strike the earth and 299 may burn up in the atmosphere. This may be a percentage of known incidents and not just unknown factors. The unknown factor is the specific rock that is yet to come.

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Without knowing the specifics involved, there could be other factors used in measuring the percentage.  For example, given various sizes and compositions of rocks, if 300 rocks have intersected the earth's orbit in the past, then 1 may strike the earth and 299 may burn up in the atmosphere.  This may be a percentage of known incidents and not just unknown factors.  The unknown factor is the specific rock that is yet to come.

This object is 1/4 of a mile long, and will not burn up completely in the atmosphere. The speed and angle of attack of the object are the two most important variables for determing the degree of burn. But the main source of uncertainty for actually hitting the Earth is the precision by which we know its orbit, and many observations are required to refine the orbital calculations.

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"Last Thursday, Dec. 23, scientists announced that a space rock named 2004 MN4 had about a 1-in-300 chance of striking Earth on April 13, 2029"

As I sit here watching the snow pile up, I wonder if their models for calculating probability are better than those of the National Weather Service.

BTW - They now have the probability at 2.6% (or about 1 in 40). Anyone have Sir Richard Branson's number at VirginGalactic?

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Is there a fundamental different between the method for calculating the probability of the asteroid hitting earth and the flip of a coin?

For the asteroid... maybe you know its orbit with a margin of error (due the precision of your instruments) of one degree, meaning the asteroid may deviate one degree from the projected path. Then we calculate, in even increments, 300 possible paths within our margin or error, and only one of those paths is a collision course with earth - the probability of the asteroid hitting earth is then 1 in 300.

For a coin or a die however, the probability is inferred from past instances of the event. In this case the probability is not dependant on the precision of any instrument; in fact no effort is taken to measure the individual event to predict its outcome.

Technically you could treat a coin and an asteroid the same way either way. You could toss a coin and scramble to measure its velocity, spin rate, vibrations, etcetera; then furiously calculate all your measurements, and in the end tack on your margin of error (hopefully less than 50% *). Or you could say... well out of the last 300 asteroids we noticed, only hit the earth; so the probability is 1 in 300.

It seems to me that these methods are both legitimate and different from each other – they can co-exist just fine. For example if, after a toss, you can calculate that the coin has a 60% chance of landing on heads, you have not disproved that the probability of any old coin being flipped is 50/50.

The difference is measuring a single event (and calculating probability from the precision of your measurements and unknown factors) vs. inferring probability from multiple instances of past events. The former method would be better to use for less frequent events and events with known factors; the latter method is better for frequent events, and events with unknown factors.

*to check my understanding of this... if the margin of error for calculating a coin landing on heads after a toss was 50% it would be the same as relying on the probability induced from past instances. This would make using the former method impractical (because it is harder ), unless our measurements were accurate enough to have a final margin of error less than 50%.

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I have a better question why is it every few months the press even does these reports about our supposed impending doom, usually by some sort of extraterestrial object, anyway? This happans all the time where some group reports some relatively high chance of impact in 2037 or 2173 or whatever and then the percentages are lowered until the story is withdrawn with a retraction. Why does it seem like the press wants the earth to be destroyed in some type of disaster? Why do they put this stuff in the science sections of most newspapers, right next to the report on the supposed rise in global warming while ignoring real science? I understand they are pushing there leftist agenda's with the global warming type stuff, but what is the point of the apocalyptic stuff? I don't think it's simply sensationalism to sell more papers either because the stories are usually buried relatively deep. So does anyone have any suggestions?

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I think how you answer the question, “Is there a fundamental difference...” depends on what level you care to take “fundamental.”

You could argue that the probability calculated from a margin of error for an asteroid has the same root as the probability of a coin toss. In both cases the assumption is being made that it is either going to be heads or tails, path #1, #2, #3... or #300; so in both cases we are inferring from past instances that their will be one out of a definite set of possible outcomes.

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Why do they put this stuff in the science sections of most newspapers, right next to the report on the supposed rise in global warming while ignoring real science?

Are you saying that the scientists who work on the Near Earth Object (NEO) program, the ones who use sophisticated equipment to observe and track NEOs, the ones who send spacecraft to rendezvous with asteroids and comets, the ones who use complex mathematics and physics to refine the orbital parameters of these objects, are not doing "real science?"

Incidentally, do you often read the science sections of these newspapers, papers say like the New York Times? Do you know how much space for science they have given to pure speculation like superstring theory? The people on the NEO program are doing science. The same cannot be said for the mathematical fantasyland of string theorists.

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Why does it seem like the press wants the earth to be destroyed in some type of disaster?

If nothing happens, it's not news. Or, if good things happens, it's not news. Ever read a story about how many students don't bring guns to school?

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This object is 1/4 of a mile long, and will not burn up completely in the atmosphere. The speed and angle of attack of the object are the two most important variables for determing the degree of burn. But the main source of uncertainty for actually hitting the Earth is the precision by which we know its orbit, and many observations are required to refine the orbital calculations.

I would think that the most important observation would be just wait till it gets closer!! The precision would go up from there.

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I would think that the most important observation would be just wait till it gets closer!!  The precision would go up from there.

It's not the distance as much as it is a sufficient number of proper observations. The orbital parameters of many of these objects can become rather complicated, and precision is narrowed as a function of the number and quality of observations made. Besides, if they wait till it is really close, then it may be too late to do anything about it. Any mission to divert the object requires a great deal of preparation, movies notwithstanding.

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I would think that the most important observation would be just wait till it gets closer!!  The precision would go up from there.
Attention is being paid to this object because it is the first to receive a Torino Impact Hazard Scale rating of 2, which would make it the most dangerous known orbiting hazard. However, the scale goes up to 10, and the description of hazard level 7 says "For such a threat in this century, international contingency planning is warranted, especially to determine urgently and conclusively whether or not a collision will occur". A rating of 2 means "a discovery, which may become routine with expanded searches, of an object making a somewhat close but not highly unusual pass near the Earth. While meriting attention by astronomers, there is no cause for public attention or public concern as an actual collision is very unlikely. New telescopic observations very likely will lead to re-assignment to Level 0 [no hazard]."

The article linked at the top of the thread was posted 1:30p Dec 27, and this article was posted by the same author at 8:15p the same day. The revised article notes that the odds actually got up to 1 in 37, but old observations provided the data that showed that impact could be ruled out. The JPL article on this impact says "When these additional observations were used to update the orbit of 2004 MN4, the uncertainties associated with this object's future positions in space were reduced to such an extent that none of the object's possible trajectories can impact the Earth (or Moon) in 2029". The hazard increases from 0 to 1 during 2035-7 (numbers here) rocketing up to a 1 in 13,000 probability.

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You could argue that the probability calculated from a margin of error for an asteroid has the same root as the probability of a coin toss.  In both cases the assumption is being made that it is either going to be heads or tails, path #1, #2, #3... or #300; so in both cases we are inferring from past instances that their will be one out of a definite set of possible outcomes.

The margin of error explanation seems confusing to me. (which is the reason for my original post)

If I measure the height of a mountain with a device that has a margin of error +/- 150 feet and the device reports a value of 12,345 ft. I wouldn't say, "there is a 1 in 300 chance the mountain is 12,345 ft tall". This is a wierd thing to say, and only makes sense if you partition the error region into 1 foot increments (there's a 1 in 600 chance if you divide the error space into .5 foot increments).

The normal way such a measurement is reported is, "the mountain is 12,345 ft tall with a margin of error of +/- 150 ft".

So in the asteroid example, the astronomers are partitioning the problem into some "error space" and 299 out of 300 do not result in a collision. What "error space" they are using?