1. A six-sided die is rolled and observe the roll. Let N, denote the event that
ID: 3324862 • Letter: 1
Question
1. A six-sided die is rolled and observe the roll. Let N, denote the event that the si. Let O denote the roll of the die is odd-numbered. Let D, denote the event that the roli is less than,j. a. What is the sample space? Determine the elements of the events O and D, b. What is P(N,ID), the conditional probability that 3 is rolled given that the roll is less than 5? c. What is the conditional probability that the roll is greater than 3 given that the roll is odd? d. What is P(D O), the conditional probability that the roll is less than 4 given that the roll is odd? e. What is POD e conditional probability that the roll is odd given it is less than 4.Explanation / Answer
(a) The sample space is {1,2,3,4,5,6} which can which represents the events that can occur on the roll of the die.
elements of O are {1,3,5} and D5 is {1,2,3,4} which represents the condition that the events are odd and where events are less than 5
(b) P(N3 | D5) = 1/4 as 3 is the only odd numer in a sample space of 4 which is less than 5
(c) Cond prob that roll is greater than 3 given that roll is odd is = 1/6 as 5 is the only number that is greater than 3 and is odd
(d) P(D4 | O) = 2/3 as 1 and 3 are the odd rolls less than 4 in a sample space of 4
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