Question

Question 1

Suppose an economic examination has 5 true or false questions and a passing grade is obtained with 3 or more correct answers. A student answered all the 5 questions by flipping a fair coin and answering true if the coin shows a head and false if it shows a tail.

a) Using the classical interpretation of probability, what is the chance the student will pass the exam?

Question 4

Bayes’ rule can be used to identify and filter spam emails and text messages.
A large collection of real SMS text messages from participating cellphone
used in this research. In this collection, 747 of the 5574 total messages
(13.40%) are identified as spam.

The word “free” is contained in 4.75% of all messages, and 3.57% of all
messages both contain the word “free” and are marked as spam.
a) What is the probability that a message contains the word “free”, given that
it is spam?
b) What is the probability that a message is spam, given that it contains the
word “free”?

Answer 1

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