question #3 try 30% 1. (20 pts) A box contains 40 diodes of which 10 are known t
ID: 3067895 • Letter: Q
Question
question #3
try 30% 1. (20 pts) A box contains 40 diodes of which 10 are known to be (a) A diode is selected at andom. What is the probability that H (b) If the first diode drawn from the box was good, what is the probability that a second diode drawn will be good? 2. (20 pts) A manu facturer of electronic equipment purchases 1000 ICs from supplier A, 2000 ICs from supplier B, and 3000 ICs from supplier C. Testing reveals that the conditional probability of an IC failing during burn-in is, for devices from each of the suppliens Pr(FIA)0.05, Pr(FIB)0.10, Pr(FIC) The ICs 0.10. from all suppliers are mixed together and one device is selected at random. Given that the device fails, what is the probability that the device came from supplier A? (30 pts) In a digital communication system, messages are encoded into the binary symbols 0 and 1. Because of noise in the system, incorrect symbols are sometimes 3. received. Suppose that the probability of a 0 being transmitted is 0.5. Further suppose that the probability of a transmitted 0 being received as a 1 is 0.05 and the probability of a transmitted 1 being received as a 0 is 0.08. Find the probability that it was I that was transmitted given that a I was received. 4. (30 pts) In a digital communication system, assume that the event of an error occurring in one binary symbol is statistically independent of the event of an error occurring in any other binary symbol. Given that the probability of an incorrect symbol being received is 0.062, what is the probability of receiving six successive symbols with no more than one error?Explanation / Answer
P(1 was received)=P(1 was transmited and 1 received)+P(0 was transmitted and 1 received)
=0.5*(1-0.08)+0.5*0.05=0.485
hence P(1 transmited|1 was received)=P(1 was transmited and 1 received)/P(1 was received)
=0.5*(1-0.08)/0.485=0.9485
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