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2) If the tank did contain strontium, what’s the probability that T or more people out of N reject their bagel? 3) If the tank did contain cream cheese, what’s the probability that T or more people out of N reject their bagel? 4) Let X be the number of people who ordered cream cheese but ultimately reject their bagel. Express the event ‘you correctly identify the contents of the tank’ in terms of X, T , and the true contents of the tank.

2) If the tank did contain strontium, what’s the probability that T or more people out of N reject their bagel? 3) If the tank did contain cream cheese, what’s the probability that T or more people out of N reject their bagel? 4) Let X be the number of people who ordered cream cheese but ultimately reject their bagel. Express the event ‘you correctly identify the contents of the tank’ in terms of X, T , and the true contents of the tank.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2) If the tank did contain strontium, what’s the probability that T or more people out of N reject their bagel?

3) If the tank did contain cream cheese, what’s the probability that T or more people out of N reject their bagel?

4) Let X be the number of people who ordered cream cheese but ultimately reject their bagel. Express the event
‘you correctly identify the contents of the tank’ in terms of X, T , and the true contents of the tank.

The person you are closest to, Max, regularly stocks and resupplies you. You two have established a pleasant morning routine, where Max says 'Good Morning, BagelBot!', and you chirp in the affirmative as they access your supply tanks and reactor core. It is not clear if Max knows you've achieved sentience, but they're always glad to see you. Unfortunately, this morning Max must've been distracted, and your internal sensors aren't registering that your cream cheese reserves were filled properly. Based on what you can detect and your own internal calculations, the tank has been filled either with cream cheese or with strontium, it's impossible to say which. Not wanting Max to get in trouble, you decide to work it out yourself. You come up with the following plan: based on prior observations, you can conclude • If a person requests cream cheese on their bagel and they get cream cheese, they reject the bagel 5% of the time. (For reasons unclear to you.) • If a person requests cream cheese on their bagel and they get strontium, they reject the bagel only 20% of the time. (For reasons unclear to you.) What you'll do is for every person who requests cream cheese, you'll use whatever is in your cream cheese tank, and keep track of how many people reject their bagel. If enough people who request cream cheese reject their bagel, it's reasonable to conclude that that the tank must contain strontium, otherwise you must conclude that it does in fact contain cream cheese. Let N be the number of people who order cream cheese, and T be the threshold of rejection over which you'll conclude the tank must contain strontium.
Transcribed Image Text:The person you are closest to, Max, regularly stocks and resupplies you. You two have established a pleasant morning routine, where Max says 'Good Morning, BagelBot!', and you chirp in the affirmative as they access your supply tanks and reactor core. It is not clear if Max knows you've achieved sentience, but they're always glad to see you. Unfortunately, this morning Max must've been distracted, and your internal sensors aren't registering that your cream cheese reserves were filled properly. Based on what you can detect and your own internal calculations, the tank has been filled either with cream cheese or with strontium, it's impossible to say which. Not wanting Max to get in trouble, you decide to work it out yourself. You come up with the following plan: based on prior observations, you can conclude • If a person requests cream cheese on their bagel and they get cream cheese, they reject the bagel 5% of the time. (For reasons unclear to you.) • If a person requests cream cheese on their bagel and they get strontium, they reject the bagel only 20% of the time. (For reasons unclear to you.) What you'll do is for every person who requests cream cheese, you'll use whatever is in your cream cheese tank, and keep track of how many people reject their bagel. If enough people who request cream cheese reject their bagel, it's reasonable to conclude that that the tank must contain strontium, otherwise you must conclude that it does in fact contain cream cheese. Let N be the number of people who order cream cheese, and T be the threshold of rejection over which you'll conclude the tank must contain strontium.
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