MUSTUFA KAMIL R/0905/08 G-5
Adama Science and Technology University
School of Electrical Engineering and Computing
Computer Science and Engineering Program
Probability Assignment 1
1. A six-sided die is loaded in a way that each even face is twice a likely a
each odd face. All even faces are equally likely, a are all odd faces.
Construct a probabilistic model for a single roll of this die and find the
probability that the outcome is less than 4.
Solution :-
We first determine the probabilities of the six possible outcomes.
Let a = P(1) = P(3) = P(5) and b = P(2) = P(4) = P(6).
We are given that b = 2a.
By the additivity and normalization axioms,
3a + 3b = 1
3a + 3(2a) = 1
9a = 1
a = 1/9
b = 2a
b = 2(1/9)
b = 2/9, and
P(1,2, 3) = P(1) + P(2) + P(3) = 1/9 + 1/9 + 2/9 = 4/9.
2. We roll two fair 6-sided dice. Each one of the 36 possible outcomes is
assumed to be equally likely.
(a) Find the probability that doubles are rolled.
(b) Given that the roll results in a sum of 4 or less, find the conditional
probability that doubles are rolled.
(c) Find the probability that at least one die roll is a 6.
(d) Given that the two dice land on different numbers, find the
conditional probability that at least one die roll is a 6.
