Probability of the Price is Right

[Guint]

The "0" rule has been in place for 11 years.

[vadernader]

The "0" rule isn't always in place.  Pricing logic should tell someone that out of 2,4,8,9,0 that, depending on the type of car, the first two digits should fall within a specific area ($24k, $28k, etc.).  From there, it's a three digit crapshoot.

Cyclone

Wait a minute, are you trying to imply the last 3 digits are a crapshoot? The "0" rule is always in place and has been for over 25 years, excluding playings that did not have a 0 in them, in which the car ended in a 5.

[JohnHolder]

OK, then how come he can assume everyone will know the "0" rule, yet not know a Nissan Versa isn't $60,000?

Mathematical probability has nothing to do with pricing skill. The fact that a contestant can figure out to rule out certain prices (i.e., a Nissan Versa obviously isn't $60k) doesn't change that. Probability is based on random occurrence.

[vadernader]

Mathematical probability has nothing to do with pricing skill. The fact that a contestant can figure out to rule out certain prices (i.e., a Nissan Versa obviously isn't $60k) doesn't change that. Probability is based on random occurrence.

You have chosen to still ignore my argument, we can't just assume every contestant will know the "0" rule but not know the first digit of a car as well.

It's clearly not just the probability of winning based on picking random numbers, it's supposed to be the probability of a contestant winning the game.

[JohnHolder]

You have chosen to still ignore my argument, we can't just assume every contestant will know the "0" rule but not know the first digit of a car as well.

It's clearly not just the probability of winning based on picking random numbers, it's supposed to be the probability of a contestant winning the game.

I'm not "ignoring" anything. You and I are talking about two different things. You're not talking about probability, you're talking about the effect of pricing skill on a contestant's chances of winning the game. Probability is, by definition, based on random selection. It doesn't change. It's not affected by the Zero Rule or a contestant's knowing or not knowing that 6 isn't the first number in the price of a Versa.

[vadernader]

I'm not "ignoring" anything. You and I are talking about two different things. You're not talking about probability, you're talking about the effect of pricing skill on a contestant's chances of winning the game. Probability is, by definition, based on random selection. It doesn't change. It's not affected by the Zero Rule or a contestant's knowing or not knowing that 6 isn't the first number in the price of a Versa.

Then I'm frankly not sure why you chose to respond to my quote saying I'm wrong and he is right because he is talking about exactly what you don't want to talk about, the odds of a contestant winning.

Not the odds of a person picking random numbers. If it was random, knowledge of the "0" rule would be moot in calculating his percentage.

[Cyclone]

Probability != pricing skill.

Cyclone

[vadernader]

Probability is a mathematical concept. It isn't affected by whether or not it's "obvious" what the price is.

Mathematical probability has nothing to do with pricing skill.

Probability != pricing skill.

Why don't you understand I'm not trying to say Probability is the same as pricing skill. I AM Trying to say that RCPlane's percentage of 19% for people who know the "0" rule is based on Pricing Skill and thus is flawed

[RCPlanes59]

Then you can use the 0.3% figure.

[Season36Fan]

Why don't you understand I'm not trying to say Probability is the same as pricing skill. I AM Trying to say that RCPlane's percentage of 19% for people who know the "0" rule is based on Pricing Skill and thus is flawed

Not necessarily.  Knowing the "0" rule can be mutually exclusive from having pricing skill, it's more like having a free number for each prize.   It's a different scenario, and a different question, so the probability is different.  One scenario/question is "What is the probability of winning with only random choices?" and the other is "What is the probability of winning with random choices, with the last number given?"   

Probabilities always involve assumptions, even if the only assumption is that there are no other assumptions. 

[Rusty]

Probability is, by definition, based on random selection. It doesn't change. It's not affected by the Zero Rule or a contestant's knowing or not knowing that 6 isn't the first number in the price of a Versa.

You're wrong.  Probability is nothing more than the ratio of the number of favorable outcomes to the number of possible outcomes.  Randomness has nothing to do with it.  A contestant knowing the zero rule increases the probability of success, since the number of possible prices (the denominator) decreases.  Knowing that the car's prices doesn't start with a 6 further increases the probability of success, again by reducing the denominator.

For a more simple example, consider Millionaire.  If a contestant rules out one of the options and makes a random guess, doesn't that contestant's probability of success change from 1/4 to 1/3?

[JokerFan]

Would someone explain to me where I went wrong with my calculations?  As I mentioned before, I don't have Inspiration 7.6 or higher, so I can't open the file.

(I think the mistake might have to do with having not factored in the fact that contestants only get ten chances.)

Assuming the 0 rule:
First prize: 1/2 chance of getting it right
Second prize: 1/6 chance of getting it right
Third prize: 1/24 chance of getting it right

1/2 + 1/6 + 1/24 = 17/24 = 70.83%

Not Assuming the 0 rule:
First prize: 1/6 chance of getting it right
Second prize: 1/24 chance of getting it right
Third prize: 1/120 chance of getting it right

1/6 + 1/24 + 1/120 = 26/120 = 21.67%

[vadernader]

Would someone explain to me where I went wrong with my calculations?  As I mentioned before, I don't have Inspiration 7.6 or higher, so I can't open the file.

(I think the mistake might have to do with having not factored in the fact that contestants only get ten chances.)

Assuming the 0 rule:
First prize: 1/2 chance of getting it right
Second prize: 1/6 chance of getting it right
Third prize: 1/24 chance of getting it right

1/2 + 1/6 + 1/24 = 17/24 = 70.83%

Not Assuming the 0 rule:
First prize: 1/6 chance of getting it right
Second prize: 1/24 chance of getting it right
Third prize: 1/120 chance of getting it right

1/6 + 1/24 + 1/120 = 26/120 = 21.67%

You can't add them, you have to multiply.

That's like saying theres a 100% chance of tossing a coin two times and having it land on heads both times.

1/2 + 1/2 = 2/2 = 100%

[Cyclone]

You're wrong.  Probability is nothing more than the ratio of the number of favorable outcomes to the number of possible outcomes.  Randomness has nothing to do with it.  A contestant knowing the zero rule increases the probability of success, since the number of possible prices (the denominator) decreases.  Knowing that the car's prices doesn't start with a 6 further increases the probability of success, again by reducing the denominator.

For a more simple example, consider Millionaire.  If a contestant rules out one of the options and makes a random guess, doesn't that contestant's probability of success change from 1/4 to 1/3?

I've seen contestants do this.  That turns out to be the correct answer.  So no, the probability is still 25% therein.

Cyclone

[Rusty]

You can't add them, you have to multiply.

That's like saying theres a 100% chance of tossing a coin two times and having it land on heads both times.

1/2 + 1/2 = 2/2 = 100%

It's been a while since I've done these, but would Ten Chances fall under the heading of geometric distribution?  Anyone who's looked at such things recently might want to give it a shot, otherwise I'll hit it after dinner (and 60 Minutes).