Question

University of Peshawar

BS Computer Science 1

st Semester

Mid term exam, Fall 2020-21

Paper : Probability and Statistics

Date: 12/02/2021

Time Allowed: 2 hours (online paper) Max. Marks: 30

Time 10:00 am to 12:00pm

Note: Attempt all questions

Section “A”

Q # 1 short questions

Q # i

a) Let X and Y be two events. Suppose that the probability that neither event occurs

is ( 3

your class #

8

 add ). What is the probability that at least one of the events

occurs?

b) Let P and Q be two events. Suppose PP  0.5, PP Q  0.2,    0.4, c P P Q  What is PQ  ?

c) The probability of Mr X living (39+add your class #) years more is ( 7

15

+add your

class #) and that of Mr Y is( 12

27

+add your class #). The probability that at least one of

them will survive (60+add your class #) years. Q # ii. (80+add your class #) Defaulting on a loan means failing to pay it back on time. The default rate among MIT students on their student loans is (23%+add your class #). As a project you develop a test to predict which students will default. Your test is

good but not perfect. It gives (29%+add your class #) false positive, i.e. predicting a

student will default who in fact will not. If has a 0% false negative rate, i.e predicting

a student won’t default who in fact will. a) Suppose random student test positive. What is the probability that he will truly

default. c) Someone offers to bet me the student in part (a) won’t default. They want me to

pay them ($225+add your class #) if the student doesn’t default and they’ll pay me

($14000+add your class #) if the student does default. Is this a good bet for me to

take?

d) In a City (25+add your class #) percent read newspaper X, (50+add your class #)

percent read newspaper Y and (83+add your class #) percent read Z (30+add your

class #) X and Y, (15+add your class #) X ans Z, (22+add your class #) percent read

Y and Z. Also (25+add your class #) percent read papers combine. What is the

percentage of people who do not read any of these newspapers.​

Answer 1

Answer:

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