Post History
#3: Post edited
by
Tim Pederick
·
2023-05-09T10:08:09Z (12 months ago)
Tweak wording.
- One is a chance of doing something. The other is a chance of *having a chance* of doing something.
- Here are some analogies that may or may not help, depending on your familiarity with the kinds of situations described.
- ---
- Analogy 1: A tabletop roleplaying game (RPG).
- Your character is sneaking down a dungeon corridor. Unfortunately, you neglected to check for traps, and a poison dart flies out of a concealed hole. You roll the dice to avoid it, but you only have **a 25% chance** of succeeding at dodging it.
- This is the “25% chance of avoiding injury”. $P\left(\mathrm{uninjured}\right)=0.25$.
- Having learned your lesson, you start checking for traps as you go. Good thing too, as there’s a pitfall trap straight after the dart trap. The game master secretly rolls your search result; there is **a 25% probability** that you see it. If you don’t, you automatically fall in. If you do see it, you still have to roll your **chance of avoiding it**.
- This is the “25% probability that there was a chance of avoiding injury”. $P\left(\mathrm{uninjured}\right)=0.25x$, where $x$ is your chance of succeeding on that second roll.
- ---
- Analogy 2: The lottery ticket
- You and three friends buy a lottery ticket together. For some reason, you don’t want to split the prize (if any). Instead, you randomly choose which of you gets any winnings. There is **a 25% chance** that the recipient is you.
This is the “25% chance of avoiding injury”. $P\left(\mathrm{recipient} ight)=0.25$.But of course, you don’t know if there *will* be any prize coming. There’s **a 25% probability** that you’re the chosen recipient, but you still have to wait until the lottery is drawn before you know what you could receive. Your ticket probably only has a small **chance of <strike>avoiding injury</strike> winning a prize**.This is the “25% probability that there was a chance of avoiding injury”. $P\left(\mathrm{winner} ight)=0.25x$, where $x$ is the chance of the lottery ticket winning something.
- One is a chance of doing something. The other is a chance of *having a chance* of doing something.
- Here are some analogies that may or may not help, depending on your familiarity with the kinds of situations described.
- ---
- Analogy 1: A tabletop roleplaying game (RPG).
- Your character is sneaking down a dungeon corridor. Unfortunately, you neglected to check for traps, and a poison dart flies out of a concealed hole. You roll the dice to avoid it, but you only have **a 25% chance** of succeeding at dodging it.
- This is the “25% chance of avoiding injury”. $P\left(\mathrm{uninjured}\right)=0.25$.
- Having learned your lesson, you start checking for traps as you go. Good thing too, as there’s a pitfall trap straight after the dart trap. The game master secretly rolls your search result; there is **a 25% probability** that you see it. If you don’t, you automatically fall in. If you do see it, you still have to roll your **chance of avoiding it**.
- This is the “25% probability that there was a chance of avoiding injury”. $P\left(\mathrm{uninjured}\right)=0.25x$, where $x$ is your chance of succeeding on that second roll.
- ---
- Analogy 2: The lottery ticket
- You and three friends buy a lottery ticket together. For some reason, you don’t want to split the prize (if any). Instead, you randomly choose which of you gets any winnings. There is **a 25% chance** that the recipient is you.
- This parallels the “25% chance of avoiding injury”. $P\left(\mathrm{recipient} ight)=0.25$.
- But of course, you don’t know if there *will* be any prize coming. There’s **a 25% probability** that you’re the chosen recipient, but you still have to wait until the lottery is drawn before you know what you could receive. Your ticket probably only has a small **chance of winning a prize**.
- This parallels the “25% probability that there was a chance of avoiding injury”. $P\left(\mathrm{winner} ight)=0.25x$, where $x$ is the chance of the lottery ticket winning something.
#2: Post edited
by
Tim Pederick
·
2023-05-09T08:35:08Z (12 months ago)
Added a second analogy.
- One is a chance of doing something. The other is a chance of *having a chance* of doing something.
Imagine a tabletop roleplaying game. Your character is sneaking down a dungeon corridor. Unfortunately, you neglected to check for traps, and a poison dart flies out of a concealed hole. You roll the dice to avoid it, but you only have **a 25% chance** of succeeding at dodging it. $P\left(A\right)=0.25$.Having learned your lesson, you start checking for traps as you go. Good thing too, as there’s a pitfall trap straight after the dart trap. The game master secretly rolls your search result; there is **a 25% probability** that you see it. If you don’t, you automatically fall in. If you do see it, you still have to roll your **chance of avoiding it**. $P\left(A ight)=0.25x$, where $x$ is your chance of succeeding on that second roll.
- One is a chance of doing something. The other is a chance of *having a chance* of doing something.
- Here are some analogies that may or may not help, depending on your familiarity with the kinds of situations described.
- ---
- Analogy 1: A tabletop roleplaying game (RPG).
- Your character is sneaking down a dungeon corridor. Unfortunately, you neglected to check for traps, and a poison dart flies out of a concealed hole. You roll the dice to avoid it, but you only have **a 25% chance** of succeeding at dodging it.
- This is the “25% chance of avoiding injury”. $P\left(\mathrm{uninjured}\right)=0.25$.
- Having learned your lesson, you start checking for traps as you go. Good thing too, as there’s a pitfall trap straight after the dart trap. The game master secretly rolls your search result; there is **a 25% probability** that you see it. If you don’t, you automatically fall in. If you do see it, you still have to roll your **chance of avoiding it**.
- This is the “25% probability that there was a chance of avoiding injury”. $P\left(\mathrm{uninjured} ight)=0.25x$, where $x$ is your chance of succeeding on that second roll.
- ---
- Analogy 2: The lottery ticket
- You and three friends buy a lottery ticket together. For some reason, you don’t want to split the prize (if any). Instead, you randomly choose which of you gets any winnings. There is **a 25% chance** that the recipient is you.
- This is the “25% chance of avoiding injury”. $P\left(\mathrm{recipient}\right)=0.25$.
- But of course, you don’t know if there *will* be any prize coming. There’s **a 25% probability** that you’re the chosen recipient, but you still have to wait until the lottery is drawn before you know what you could receive. Your ticket probably only has a small **chance of <strike>avoiding injury</strike> winning a prize**.
- This is the “25% probability that there was a chance of avoiding injury”. $P\left(\mathrm{winner}\right)=0.25x$, where $x$ is the chance of the lottery ticket winning something.
#1: Initial revision
by
Tim Pederick
·
2023-05-01T23:58:01Z (12 months ago)
One is a chance of doing something. The other is a chance of *having a chance* of doing something. Imagine a tabletop roleplaying game. Your character is sneaking down a dungeon corridor. Unfortunately, you neglected to check for traps, and a poison dart flies out of a concealed hole. You roll the dice to avoid it, but you only have **a 25% chance** of succeeding at dodging it. $P\left(A\right)=0.25$. Having learned your lesson, you start checking for traps as you go. Good thing too, as there’s a pitfall trap straight after the dart trap. The game master secretly rolls your search result; there is **a 25% probability** that you see it. If you don’t, you automatically fall in. If you do see it, you still have to roll your **chance of avoiding it**. $P\left(A\right)=0.25x$, where $x$ is your chance of succeeding on that second roll.