Blonde, bleached blonde (H). You have high standards with respect to truthin advertising, particularly when it comes to hair color. One day at the laun-dromat, you meet an attractive blonde stranger named Chris and wonder ifyou should pursue a relationship. Unfortunately, you have the nagging beliefthat Chris's golden locks may have been the result of peroxide-presentingthe specter of a dark (haired) future. However, you also know several factsabout the incidence of dyed hair and about your ability to detect fraudulentfollicles. You know that 90% of blonde people in the world are naturallyblonde. You have done a personal survey and learned that you are 80% accu-rate in your ability to correctly categorize fake hair color as fake and realhair color as real. What is the probability that Chris's hair is fair and thatbleached beliefs were incorrect? Given these facts, should you pursueyouryour relationship with Chris?

Answered: Blonde, bleached blonde (H). You have…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Blonde, bleached blonde (H). You have high standards with respect to truth
in advertising, particularly when it comes to hair color. One day at the laun-
dromat, you meet an attractive blonde stranger named Chris and wonder if
you should pursue a relationship. Unfortunately, you have the nagging belief
that Chris's golden locks may have been the result of peroxide-presenting
the specter of a dark (haired) future. However, you also know several facts
about the incidence of dyed hair and about your ability to detect fraudulent
follicles. You know that 90% of blonde people in the world are naturally
blonde. You have done a personal survey and learned that you are 80% accu-
rate in your ability to correctly categorize fake hair color as fake and real
hair color as real. What is the probability that Chris's hair is fair and that
bleached beliefs were incorrect? Given these facts, should you pursue
your
your relationship with Chris?

Expert Solution

Step 1

Given that 90% of blonde people in the world are naturally blonde. We can correctly guess natural hair as natural, and fake hair as fake, 80% of the time. We are suspicious in two cases;

case:1

If the blond person is a natural blond (0.9 chance) chance, we have a 0.2 (1- 0.8= 0.2) chance of guessing incorrectly that the hair is natural when it is in fact fake.

Case:2

If the blond person is not a natural blond (1-0.9 = 0.1 chance), there is a 0.8 chance of us guessing that the hair is fake.

Now

when we add those two cases, we are suspicious about:

0.9 * $(0.9 \times 0.2) + (0.1 \times 0.8) =$ 0.26 or 26% of times.