EE3533 has 43 registered students who incdices are from 1 to 43. We randomly pic
ID: 3277349 • Letter: E
Question
EE3533 has 43 registered students who incdices are from 1 to 43. We randomly pick a lucky student for the exemption. Let N1 devote the event that the lucky index is t. Let O denote the odd-numbered lucky index. Let Dj denote the event that the lucky index is less than j
a. What is the sample space? Determine the number of elements of the events O and the elemtns of the vents D5 .
b. What is the P( N17 | D35 ), the conditional probability that index 17 is picked given the lucky index is less than 35?
c. What is the conditional probability that the index is greater than 39 given that the index is odd?
d. What is P(O|D7), the conditional probability that the lucky index is odd given it is less than 7?
EE3333 has 43 registered students whose indices are from I to 43 We randomly pick a lucky student for the exam exemption. Let N, denote the event that the lucky index is t. Let O denote the edd-numbered lucky index. Let D denote the event that the lucky index is less than y a. What is the sample space? Determine the number of elements of the events O and the elements of the events D b. What is PN Ds), the conditional probablity that iodex 17 is picked given c. What is the conditional probabulity that the undex is greater than 39 given d. What is PiO D), the conditional probablity that the hicky index is odd that the lucky index is less than 35? that the index is odd? given it is less than 7Explanation / Answer
(a) Sample space = 43
n(O) = 22 (22 odd numbers in 1 to 43)
n(D5) = 4 (numbers less than 4)
(b)
P(D35) = 34/43
P(N17 and D35) = 1/43
P(N17|D35) = P(N17 and D35)/P(D35) = 1/34
(c)
P(greater than 39 and index is odd) = 2/43
Required probability = (2/43) / (22/43) = 1/11
(d)
P(O|D7) = P(O and D7)/P(D7)
P(O and D7) = 3/43
P(D7) = 6/43
P(O|D7) = 3/6 = 1/2
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