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' ‘ Consider an urn with hfltwo white, and two blue marbles. You randomly draw the marbles out one by one and note
. their color (you do not I ace the . bles once they are drawn). Calculate the probability that you draw them out in the following order. red, white’rred, white blue
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Consider a digital data transmission system which is designed’to transmit only three symbols X,Y, and Z. Each of the three
. symbols is equally likely to be transmitted. Due to noise in the system, if one of the three signals is transmitted, the
probability of the receiver correctly detecting the symbol transmitted 1s 0 88. In other words, if one of the three symbols 13
transmitted, the probability of the detector at the receiver incorrectly detecting one of. the other two symbols (and thus
introducing an error) 1S 0.12. (f , (a) If symbol Z is detected at the receiver, what is. the probability that symbol Z was actually transmitted ?
(b) If symbol X is detected at the receiver, what is the probability that symbol Y was actually transmitted ? 2-4: 1—-L—"~”J 2‘4:- Mamie. +PcAMS—Lu-L42-l-za29- —s‘—1—M—‘°°\3‘I . - WM _ Y u P (3:12 Pug: Wag :. g _ games-1:4: 22> Jrrcwmktm W
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subsystems operate independently Furthermore, assume each subsystem operates properly with probability 0.8. Calculate the
probability of the overall system operating properly. ‘ N 0'06 \3
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When a parent walks in alone, they make a sale 15% of the time. However, when a student and a parent walk in together, they
make a sale of 30% of the time. When the door to the store opens, 40% of the time a student enters, either alone or with a
parent; and 90% of the time a parent enters, either alone or with a student. Define the relevant events as follows : S (student
walks in), P (parent walks in), and C (a computer is sold). For each time the door opens, calculate the probability that a computer will be sold.
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