Question

In: Statistics and Probability

One percent of the people in Westeros belong to the secret Brotherhood society. The Chief Interrogator...

  1. One percent of the people in Westeros belong to the secret Brotherhood society. The Chief Interrogator of Westeros (“the tickler”) has a 95% chance of ruling that an interrogated person belongs to the Brotherhood, when indeed this person is one of its members. For people who are not members, “the tickler” deems them trustworthy (i.e., not a member of the Brotherhood) with probability 0.4. Suppose “the tickler” interrogates a random person from Westeros and finds them guilty of belonging to the Brotherhood. What is the probability that this person indeed belongs to the Brotherhood?

Solutions

Expert Solution

We are given,

P(actually belong to Brotherhood) = 1% = 0.01

P(actually dont belong to Brotherhood) =1 - 0.01 = 0.99

P(Tickler says belong to Brotherhood | actually belong to Brotherhood) = 95% = 0.95

P(Tickler says dont belong to Brotherhood | actually belong to Brotherhood) = 1 - 0.95 = 0.05

P(Tickler says dont belong to Brotherhood | actually dont belong to Brotherhood ) = 0.4

P(Tickler says belong to Brotherhood | actually dont belong to Brotherhood ) = 1 - 0.4 = 0.6

We need to find :

Probability that the person indeed belongs to the Brotherhood given that Tickler says he belong to Brotherhood

= P(Actually belongs to brotherhood and Tickler says he belong to Brotherhood) / P(Tickler says he belong to Brotherhood)

Now,

P(Tickler says he belong to Brotherhood) =

= P(actually belong to Brotherhood)* P(Tickler says belong to Brotherhood | actually belong to Brotherhood) +

P(actually dont belong to Brotherhood) * P(Tickler says belong to Brotherhood | actually dont belong to Brotherhood )

= 0.01* 0.95 + 0.99*0.6

= 0.6035

P(Actually belongs to brotherhood and Tickler says he belong to Brotherhood) =

= P(actually belong to Brotherhood)* P(Tickler says belong to Brotherhood | actually belong to Brotherhood)

= 0.01*0.95 = 0.0095

Probability that the person indeed belongs to the Brotherhood given that Tickler says he belong to Brotherhood =

= 0.0095 / 0.6035

= 0.0157

orchestra answered 2 years ago
Next > < Previous

Related Solutions

One percent of the people in Westeros belong to the secret Brotherhood society. The Chief Interrogator...
One percent of the people in Westeros belong to the secret Brotherhood society. The Chief Interrogator of Westeros ("the tickler") has a 95% chance of ruling that an interrogated person belongs to the Brotherhood, when indeed this person is one of its members. For people who are not members, \the tickler" deems them trustworthy (i.e., not a member of the Brotherhood) with probability 0.4. Suppose "the tickler" interrogates a random person from Westeros and finds them guilty of belonging to...
Suppose that there are n people in a group, each aware of a different secret no...
Suppose that there are n people in a group, each aware of a different secret no one else in the group knows about. These people communicate by phone; when two people in the group talk, they share information about all secretes each knows about. For example, on the first call, two people share information, so by the end of the call, each of them knows about two secretes. The gossip problem asks for the number of phone calls that are...
A “sick society”? One way of interpreting the statistic that at least 12 percent of children...
A “sick society”? One way of interpreting the statistic that at least 12 percent of children suffer from a mental disorder is to argue that “something is wrong with our society.” If there is something wrong, what is it? Ineffective parenting? Insufficient research support for effective treatments? Apathy? After identifying some of the societal problems leading to mental disorders of childhood, you can ask about solutions. Should parenting classes be required? Should more money be spent on research? Should children...
Steganography is the technique of hiding secret messages/information within other non-secret data/information. One popular way of...
Steganography is the technique of hiding secret messages/information within other non-secret data/information. One popular way of steganography is hiding text (plaintext) within images (cover text). Each image is a collection of pixels, where each pixel is typically represented by 3 values (RGB). Each of R, G, and B is a value between 0 and 255 and thus can be represented by 8 bits. The color of the pixel depends on these values. However, if the least significant bit (last bit...
______23. The chief disadvantage of handouts is that A. people don’t read them. B. people don’t...
______23. The chief disadvantage of handouts is that A. people don’t read them. B. people don’t keep them. C. they are useful only with large groups. D. people read them while you are speaking. ______24. In today’s business environment, overhead transparencies are A. obsolete and no longer used. B. still preferred by some professionals. C. impossible to create. D. none of the above. ______25. To hold your audience’s attention during the body of your speech, A. make at least seven...
How relevant is the Maslow Theory to people in today’s society?
How relevant is the Maslow Theory to people in today’s society?
The One Device: The Secret History of the iPhone Review 1. Discuss the significance of the...
The One Device: The Secret History of the iPhone Review 1. Discuss the significance of the Apple supply chain and the materials that go into making the iPhone. 2. How much waterloos into producing 1 billion iPhones? 3. How did one son's search for a way to ease his mother's chronic pain help lead to touchscreen functionality for the iPhone? Considering that, is Apple's claim that it invented multitouch valid? 4. Know about the significance of the Atacama Desert and...
In marketing, for consumer behavior, which adopter category do most people belong to? Does this differ...
In marketing, for consumer behavior, which adopter category do most people belong to? Does this differ with different product categories? Is age a factor in innovation behavior?
List the benefits that organic food provides to people, the environment, and society.
List the benefits that organic food provides to people, the environment, and society.
The following measures belong to one of the four perspectives of the balanced scorecard: 1) Return...
The following measures belong to one of the four perspectives of the balanced scorecard: 1) Return on investment 2) Marketing time 3) Number of new customers 4) Percentage of income from new sources 5) Quality costs 6) Employee productivity Required: a. Identify the appropriate perspective for each measure listed above. b. Suggest a possible strategic objective that could be associated with each measure (Be sure to clearly label each article)
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT