MAT271E Probability and Statistics: Homework 1
Asst. Prof. Barış Başpınar
March 16, 2022
Due date: March 30, 2022
Policy: You should write your own answer/code by yourself. Cheating is highly discouraged; it
will mean a zero or negative grade from the homework.
Submission Instructions: Please submit your homework through the Ninova website. Please zip
and upload all your files using filename studentID.rar. For the questions that require to write a
Matlab code, you must provide all Matlab codes you wrote with your zipped file. The codes you
do not submit will cause you to lose a portion of your grade. You must include the report.pdf file
with your homework containing answers to the questions, and outputs/figures.
Question 1:
There are 8 adults and 5 children in a group of people. Assume that we choose randomly 4 of these
people to form a new group. Calculate the probability that new group has
a) 3 adults and 1 child
b) 4 adults
c) at least 2 children
Question 2:
In a group of students, 60% of students are enrolled to the probability course. We choose randomly
8 of them. Calculate the probability that
a) exactly 5 students are enrolled to the course
b) at least 6 students are enrolled to the course
Question 3:
A family has 2 children, and
a) we see one of their children in the market and realize that he is a boy. What is the
probability that both children are boys?
b) the family states that at least one of the children is a boy. What is the probability that both
children are boys?
c) Compare the obtained results in part a and part b, and discuss your findings.
Question 4:
There are two different boxes. The first one contains 3 red and 5 blue balls, while the other one
contains 7 red and 4 blue balls. One ball is drawn randomly from one of the boxes, and we know
that it is blue. What is the probability that it is drawn from the first box?
