explain xkcd - User contributions [en]

1252: Increased Risk

2013-08-16T11:44:19Z

Yetanotheruseraccount: /* Explanation */

{{comic
| number = 1252
| date = August 16, 2013
| title = Increased Risk
| image = increased_risk.png
| titletext = You may point out that strictly speaking, you can use that statement to prove that all risks are tiny--to which I reply HOLY SHIT WATCH OUT FOR THAT DOG!
}}

==Explanation==
{{incomplete}}

The panel (specifically [[Cueball]]) satirises the common (mis?)understanding of the concept of percentage. Quoting a percentage figure, without mentioning the base which this ratio acts on - is meaningless (outside of arithmetic for arithmetic's sake). Most everyday communication however, succumbs to such incompleteness. In the aftermath of this ambiguity, people tend to conflate relative and absolute changes. This seems to particularly irk [[Randall]], who's documented his disgust [[1102|twice]] [[985|before]].

If the probability of a shark attack at the North beach is 0.000001 (one in a million), then the probability of shark attack at the South beach is still 0.0000012 (1.2 in a million). The difference between these values is not enough to normally justify choosing one beach over the other. Cueball parodies the concern by noting that by going a third time their chance of attack by dogs with shotguns increases by 50%. This is correct. If the chance of the dog attack is 0.000000001 (one in a billion) on each visit to the beach, then in after two visits the chance of attack is is about 0.000000002 whereas after three visits it becomes 0.000000003, a 50% increase.

Beret further misunderstands probability by believing that - since they haven't been attacked in their first two trips, the chance of attack by dogs with shotguns is much higher on their third outing.

The title text discusses the argument that, if a tiny risk increased by 50% is still tiny, then since any probability can be reached by repeatedly increasing by 50%, then any probability is "tiny". Randall is about to debate this when he is apparently attacked by a dog.

==Transcript==
:Ponytail: We should go to the north beach. Someone said the south beach has a 20% higher risk of shark attacks.
:Cueball: Yeah, but statistically, taking three beach trips instead of two increases our odds of getting shot by a swimming dog carrying a handgun in its mouth by '''''50%!'''''
:Beret Guy: Oh no! This is our third trip!
:[Reminder: A 50% increase in a tiny risk is ''still tiny''.]

{{comic discussion}}

Firstly, the 50% increase in risk is only if the probabilities of being shot by a shotgun wielding swimmer-dog, on each beach trip are independent events. In the same paranoid storyline where such a dog exists, it would also almost certainly be controlled by the black ops agency of a national government - who would already have deployed the dog to spy on you, during your first two trips. Cumulative learning is just one of the many, many variables tat would result in a probability increase for death-by-canine which is different than 50%.

Secondly, the title text has me intrigued. Yes, 'tiny' is a weasel word, but how can you use the statement below the panel to show that ALL risks are tiny?

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Ponytail]]
[[Category:Comics featuring Beret Guy]]
[[Category:Friday comics]]
[[Category:Comics from August]]
[[Category:Math]]

1252: Increased Risk

2013-08-16T11:43:19Z

Yetanotheruseraccount:

{{comic
| number = 1252
| date = August 16, 2013
| title = Increased Risk
| image = increased_risk.png
| titletext = You may point out that strictly speaking, you can use that statement to prove that all risks are tiny--to which I reply HOLY SHIT WATCH OUT FOR THAT DOG!
}}

==Explanation==
{{incomplete}}

The panel (specifically [[Cueball]]) satirises the common (mis?)understanding of the concept of percentage. Quoting a percentage figure, without mentioning the base which this ratio acts on - is meaningless (outside of arithmetic for arithmetic's sake). Most everyday communication however, succumbs to such incompleteness. In the aftermath of this ambiguity, people tend to conflate relative and absolute changes. This seems to particularly irk [[Randall]], who's documented his disgust [[twice|1102]] [[before|985]].

If the probability of a shark attack at the North beach is 0.000001 (one in a million), then the probability of shark attack at the South beach is still 0.0000012 (1.2 in a million). The difference between these values is not enough to normally justify choosing one beach over the other. Cueball parodies the concern by noting that by going a third time their chance of attack by dogs with shotguns increases by 50%. This is correct. If the chance of the dog attack is 0.000000001 (one in a billion) on each visit to the beach, then in after two visits the chance of attack is is about 0.000000002 whereas after three visits it becomes 0.000000003, a 50% increase.

Beret further misunderstands probability by believing that - since they haven't been attacked in their first two trips, the chance of attack by dogs with shotguns is much higher on their third outing.

The title text discusses the argument that, if a tiny risk increased by 50% is still tiny, then since any probability can be reached by repeatedly increasing by 50%, then any probability is "tiny". Randall is about to debate this when he is apparently attacked by a dog.

==Transcript==
:Ponytail: We should go to the north beach. Someone said the south beach has a 20% higher risk of shark attacks.
:Cueball: Yeah, but statistically, taking three beach trips instead of two increases our odds of getting shot by a swimming dog carrying a handgun in its mouth by '''''50%!'''''
:Beret Guy: Oh no! This is our third trip!
:[Reminder: A 50% increase in a tiny risk is ''still tiny''.]

{{comic discussion}}

Firstly, the 50% increase in risk is only if the probabilities of being shot by a shotgun wielding swimmer-dog, on each beach trip are independent events. In the same paranoid storyline where such a dog exists, it would also almost certainly be controlled by the black ops agency of a national government - who would already have deployed the dog to spy on you, during your first two trips. Cumulative learning is just one of the many, many variables tat would result in a probability increase for death-by-canine which is different than 50%.

Secondly, the title text has me intrigued. Yes, 'tiny' is a weasel word, but how can you use the statement below the panel to show that ALL risks are tiny?

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Ponytail]]
[[Category:Comics featuring Beret Guy]]
[[Category:Friday comics]]
[[Category:Comics from August]]
[[Category:Math]]

Talk:1252: Increased Risk

2013-08-16T10:40:36Z

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2013-08-16T10:16:59Z

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Increased Risk

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1252: Increased Risk

2013-08-16T10:08:54Z

Yetanotheruseraccount:

File:increased risk.png

2013-08-16T10:08:22Z

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File:increased risk.png

2013-08-16T10:08:06Z

Yetanotheruseraccount: Yetanotheruseraccount uploaded "File:increased risk.png"

http://imgs.xkcd.com/comics/increased_risk.png

File:increased risk.png

2013-08-16T10:06:44Z

Yetanotheruseraccount: Created page with "http://imgs.xkcd.com/comics/increased_risk.png"

http://imgs.xkcd.com/comics/increased_risk.png