**The Accuracy of the iPhone X’s Fingerprinting Sensor**The iPhone X’s fingerprinting sensor claims to detect forged fingerprints with high accuracy. Users consider the sensor to be very reliable if it can identify forged fingerprints in 99 out of 100 attempts. However, if a person is not forging their fingerprint, the sensor has a false positive rate, incorrectly indicating a forged fingerprint in 1 out of 1000 attempts. Let's assume that one out of every 1 million iPhone X users is a fraud. By applying Bayes' rule, we can compute the probability that if the fingerprint sensor detects a fraudulent fingerprint, the iPhone user is indeed a fraud.To summarize:- Detection accuracy (P(Forged | Fraud)) = 99 / 100 = 0.99- False positive rate (P(Forged | Not Fraud)) = 1 / 1000 = 0.001- Base rate of fraud (P(Fraud)) = 1 / 1,000,000 = 0.000001- Base rate of non-fraud (P(Not Fraud)) = 1 - P(Fraud) = 0.999999Using Bayes' rule:\[ P(Fraud | Forged) = \frac{P(Forged | Fraud) \times P(Fraud)}{P(Forged)} \]Where \( P(Forged) \) can be calculated as:\[ P(Forged) = P(Forged | Fraud) \times P(Fraud) + P(Forged | Not Fraud) \times P(Not Fraud) \]Plugging in the values:\[ P(Forged) = (0.99 \times 0.000001) + (0.001 \times 0.999999) \]\[ P(Forged) = 0.00000099 + 0.000999999 \]\[ P(Forged) \approx 0.001000989 \]Now, applying Bayes' rule:\[ P(Fraud | Forged) = \frac{0.99 \times 0.000001}{0.001000989} \approx \frac{0.00000099}{0.001000989} \approx 0.000989 \]Therefore, the probability that the user is a fraud, given that the fingerprint sensor detects a forged fingerprint, is roughly 0.

Define the events, A : Iphone X detects fingerprint as forged B : The person is a fraud Given, if a…

The Iphone X's fingerprinting sensor claims to detect forged fingerprints accurately. The user of Iphone X will consider the sensor very accurate if the sensor can detect forged fingerprints 99 out of 100 attempts. But, if the person is not forging the fingerprint, it will incorrectly indicate that it can detect forged fingerprint 1 out of 1000 attempts. Lets assume that one out of every 1 million Iphone users is a fraud. Use Bayes rule to compute the probability that if the fingerprint sensor detects the fraud fingerprint, then the iphone user is indeed a fraud.

The Iphone X's fingerprinting sensor claims to detect forged fingerprints accurately. The user of Iphone X will consider the sensor very accurate if the sensor can detect forged fingerprints 99 out of 100 attempts. But, if the person is not forging the fingerprint, it will incorrectly indicate that it can detect forged fingerprint 1 out of 1000 attempts. Lets assume that one out of every 1 million Iphone users is a fraud. Use Bayes rule to compute the probability that if the fingerprint sensor detects the fraud fingerprint, then the iphone user is indeed a fraud.

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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