Engineering Probability & Statistics
Sharif University of Technology
Hamid R. Rabiee & S. Abbas Hosseini
September 20, 2014
CE 181
Date Due: Mehr 12st , 1393
Homework 1 (Chapter 1 , 2)
Problems
1. Enroll the “Engineering Probability & Statistics” in www.piazza.com.
2. Prove for any collection of events A1 , ..., An :
P(
n
[
Ai ) ≤
i=1
n
X
P (Ai )
i=1
3. Suppose that 10 fish are caught at a lake that contains 5 distinct types of fish.
a. How many different outcomes are possible, where an outcome specifies the numbers of caught
fish of each of the five types.
b. How many outcomes are possible when 3 of the 10 fish caught are trout?
c. How many when at least 2 of the 10 are trout?
4. Propose a method to simulate a fair coin using an unfair coin.
5. A bowl contains 10 balls numbered 1 through 10. Four balls are drawn without replacement.
What is the probability that the second largest number drawn will be 6?
6. A point (x, y) is to be selected from the square S containing all points (x, y) such that 0 ≤ x ≤ 1
and 0 ≤ y ≤ 1. Suppose that the probability that the selected point will belong to each specified
subset of S is equal to the area of that subset. Find the probability of each of the following
subsets:
a. the subset of points such that (x − 12 )2 + (y − 12 )2 ≥ 4;
b. the subset of points such that y ≤ 1 − x2 ;;
c. the subset of points such that x = y.
7. If the probability that student A will fail a certain statistics examination is 0.5, the probability
that student B will fail the examination is 0.2, and the probability that either student A or B
will fail the examination is 0.6, what is the probability that exactly one of the two students will
fail the examination?
8. If n people are seated in a random manner in a row containing 2n seats, what is the probability
that no two people will occupy adjacent seats?
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