Probability of the Price is Right

[PriceFanArmadillo]

Right, but that formula is much easier to use to calculate the full probability.  Here we go:

One roll, with P₁=.25: (1-(1/2))^5.

Two rolls, with P₂=.5: (1-(1/4))^5.

Three rolls, with P₃=.25: (1-(1/8))^5.

Add them together and you get a total of 25.56%.

[parliboy]

Regarding the Let'em Roll subsection of this thread, I'm going to copy what I wrote for GSF a few years ago:

(1 - (.5 ^ n)) ^ c, where n is the number of rolls remaining, and c is the number of cubes to be rolled.

[sideshowPA]

Yes, you said the exact same thing on page 1 of this thread in July of 2009.  That's not about to stop me from caring about probabilities, since I don't have a Bachelor's in pricing knowledge.  

LOL.  Wow, time flies.  I got to be arrogant twice in one thread?  That rivals Steve!

[RCPlanes59]

I figured out Ten Chances!

Short answer: 55/288 (19.1%), assuming knowledge of the zero rule.
Medium answer: Basically, I created a chart that analyzed every possibility. There was a 1/12 chance of winning the first two prizes with 2 or 8 chances used (each) and a 2/12 chance of winning the first two prizes with 3, 4, 5, 6, or 7 chances (each). From there, grunt work.
Long answer: If you have Inspiration 7.6 or higher, here's a file fully detailing what I did.
http://www.mediafire.com/?47xp9e2px9f22dc

Bear in mind, the zero rule would imply that there are 2 possibilities of the first prize, 6 possibilities of the second prize, and 24 possibilities of the third prize. Without the zero rule, that changes to 6, 24, and 120, meaning that without the zero rule, you have a 55/288 * 1/60 = 11/3456, or 0.32% chance.

[JokerFan]

I can't open the file.  I either get a message saying the file can't be open or if I try an option to open it with Microsoft Word all I get is a lot of weird characters and other nonsense.

EDIT: Reviewing your comment, I realize it is most likely because I do not have Inspiration 7.6 or higher (I don't even know what that is).  If there is no way for me to open the file, would it be possible for either a post or an Excel spreadsheet or something else?

[vadernader]

I figured out Ten Chances!

Short answer: 55/288 (19.1%), assuming knowledge of the zero rule.
Medium answer: Basically, I created a chart that analyzed every possibility. There was a 1/12 chance of winning the first two prizes with 2 or 8 chances used (each) and a 2/12 chance of winning the first two prizes with 3, 4, 5, 6, or 7 chances (each). From there, grunt work.
Long answer: If you have Inspiration 7.6 or higher, here's a file fully detailing what I did.
http://www.mediafire.com/?47xp9e2px9f22dc

Bear in mind, the zero rule would imply that there are 2 possibilities of the first prize, 6 possibilities of the second prize, and 24 possibilities of the third prize. Without the zero rule, that changes to 6, 24, and 120, meaning that without the zero rule, you have a 55/288 * 1/60 = 11/3456, or 0.32% chance.

Sorry to interject here but this is a bunch of bologna. Are you really saying there are 24 possibilities for a Car? That's just stupid. If the digits are 1 3 4 6 0 for a Nissan Versa, it's OBVIOUS what the first digit is....Come on now. I know you might find it fun/enjoyable doing all this probably stuff but please at least get it right.

[JokerFan]

We're assuming that contestants aren't that bright, and therefore a contestant could pick something like $61,340 for the price of a car (and Bob/Drew would allow the guess).

[vadernader]

We're assuming that contestants aren't that bright, and therefore a contestant could pick something like $61,340 for the price of a car (and Bob/Drew would allow the guess).

How can you assume someone will think a Nissan Versa is $60,000 yet they know the 0 rule?

[JokerFan]

I assume that's why two probabilities were given: one for knowing the 0 rule and one for not knowing the 0 rule

[Cyclone]

Sorry to interject here but this is a bunch of bologna. Are you really saying there are 24 possibilities for a Car? That's just stupid. If the digits are 1 3 4 6 0 for a Nissan Versa, it's OBVIOUS what the first digit is....Come on now. I know you might find it fun/enjoyable doing all this probably stuff but please at least get it right.

Let's use simple probability.  Let's assume the numbers 1 2 3 4 5 for the sake of example.

The first digit can be any of 5 digits.  The second digit can be any of four remaining digits.  This gives 20 possibilities for the first two digits (5 x 4).  There are three digits left for the third digit in any of those 20 options, so 20 x 3 = 60.  Then there are two options for the fourth spot; 60 x 2 = 120.  The fifth digit is the only option, so it doesn't affect anything.

In practicality, there are 120 different options available for the price of that car.

Now comes the question of contestant intelligence (and yes, some haven't really displayed any of that lately, just blame the lights and cameras).  Let's go back to using 1 3 4 6 0.  Let's go with the assumption - for now - that it can't be a $30,000 car (I am merely speculating as I am not as familiar with U.S. pricing).  This means 1 must be the first digit.  Let's also assume that the price of the car is a round figure.  Therefore, it ends in a 0 (yes, we've seen some ending "97" or "84" or such lately, but let's go with this).  Since we're reducing the five options on the first digit to one option, we've eliminated the 5 from the equation.  120 / 5 = 24.  By placing the 0 at the end, we've eliminated the 4 from the probability as we've fixed both digits and are only doing probability on the middle three.  Therefore, 24 / 4 = 6.  There are indeed only 6 ways to rearrange the 3, 4, and 6.

Let's go to logic now.  Is the Nissan only a $16,000 vehicle?  Maybe not.  Therefore, the first digit is a 3 and we are right back where we started arranging the 1, 4, and 6 in the middle.

If Mike and co. were to pick some stupid ending digit, then the game is literally almost unwinnable.  Having to pick from prices like $31,406 and $34,608 makes the game almost impossible as there would again be 24 possible ways to win even with the 3 in the first position.  They count on that different last digit to control the budget.

So, I quote you again:

Sorry to interject here but this is a bunch of bologna. Are you really saying there are 24 possibilities for a Car? That's just stupid. If the digits are 1 3 4 6 0 for a Nissan Versa, it's OBVIOUS what the first digit is....Come on now. I know you might find it fun/enjoyable doing all this probably stuff but please at least get it right.

Yes, there are 24 possibilities for a car.  Work shown above.

Cyclone

[JohnHolder]

Sorry to interject here but this is a bunch of bologna. Are you really saying there are 24 possibilities for a Car? That's just stupid. If the digits are 1 3 4 6 0 for a Nissan Versa, it's OBVIOUS what the first digit is....Come on now. I know you might find it fun/enjoyable doing all this probably stuff but please at least get it right.

He did get it right. Probability is a mathematical concept. It isn't affected by whether or not it's "obvious" what the price is. Of course a contestant who knows what they're doing is more likely to win the game (which is why it's won more than once every 24 playings), but that doesn't mean the probability changes.

[RCPlanes59]

Probabilities on this thread are considered before pricing skill. Obviously, Ten Chances is won more than 19% of the time because contestants can use pricing skill to determine the prices of these prizes. However, if they blindly went in with no idea, they would have a 19% chance of winning. However, if they didn't use the 0 rule, they would only have a 0.3% chance at winning.

This is one reason why this girl won:

[Cyclone]

Probabilities on this thread are considered before pricing skill. Obviously, Ten Chances is won more than 19% of the time because contestants can use pricing skill to determine the prices of these prizes. However, if they blindly went in with no idea, they would have a 19% chance of winning. However, if they didn't use the 0 rule, they would only have a 0.3% chance at winning.

This is one reason why this girl won:

She finally listened to some bloke in the audience?

Cyclone

[vadernader]

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

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

[Cyclone]

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

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