# Cookie Question: Ratio of Diameter to Thickness and Uncertainty

• Hi.O303
In summary, the conversation is about a homework problem involving finding the ratio of the diameter to the thickness of a chocolate chip cookie and its uncertainty. The person asking the question tried to solve it by dividing the given values, but their answer differed from the given answer. The expert then suggests getting the largest and smallest possible ratios and explains the concept of adding percent error when doing multiplication or division. The conversation ends with a clarification on the accuracy of the numbers given.
Hi.O303
I saw similar types of problems like this using Google search, but none of them answered this question specifically.

## Homework Statement

As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.5 +/- 0.02 cm and a thickness of 0.050 +/- 0.005 cm.

Find the ratio of the diameter to the thickness and the uncertainty in this ratio.

## The Attempt at a Solution

So what I did was just put 8.50 +/- 0.02 cm divided by 0.050 cm. My answer was :
170 +/- 4cm

Their answer was : 170 +/- 20 cm.

So I see where they got the 170 from, but I'm not sure why they 20cm is there.

In such questions, try to get the biggest ratio possible and the smallest one.

Okay, I did that and I got the two answers : 154.9 and 188.4, but the difference between them isn't 20.

They seem to be rounding the error to one significant figure.

Have you been told about adding the percent error when doing multiplication or division?

EDIT:
Okay, I did that and I got the two answers : 154.9 and 188.4, but the difference between them isn't 20.

Just FYI, those numbers are a little off. For example,
8.48/0.055 = ____? (slightly less than the 154.9 you gave)

## What is the Cookie Question?

The Cookie Question, also known as the Monty Hall problem, is a famous probability puzzle named after the game show "Let's Make a Deal." It involves a game show contestant who is given the choice between three doors, behind one of which is a valuable prize. After the contestant chooses a door, the host reveals one of the other doors to be a dud. The contestant is then given the opportunity to switch their choice to the remaining door. The question is, is it more advantageous for the contestant to switch or to stick with their original choice?

## Why is the Cookie Question so confusing?

The Cookie Question can be confusing because it goes against our intuition. Many people assume that since the contestant has a 1 in 3 chance of choosing the correct door at the beginning, they still have a 1 in 3 chance after one of the doors is revealed to be a dud. However, by switching their choice, the contestant actually increases their chances of winning to 2 in 3.

The correct answer to the Cookie Question is to switch your choice. By switching, you increase your chances of winning from 1 in 3 to 2 in 3. This has been mathematically proven and is known as the "Monty Hall problem solution."

## Does the Cookie Question have real-world applications?

While the Cookie Question may seem like a simple puzzle, it actually has real-world applications in fields such as statistics, game theory, and decision-making. It teaches us about the importance of understanding probability and how our intuition can sometimes lead us astray.

## Are there any variations of the Cookie Question?

Yes, there are many variations of the Cookie Question that involve different scenarios and numbers of doors. Some variations also involve multiple rounds of decision-making. However, the underlying principle remains the same: switching your choice increases your chances of winning.

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