A digital communication system sends 1\'s and 0\'s in sequence with the probabil

Question

A digital communication system sends 1's and 0's in sequence with the probability of transmitter the sending a 1 is 0.45. Errors are made in the communication channel, so the probability of receiving a 0 given that a l was sent is 0.03, and the probability of receiving a given that a 0 was sent is 0.02. a. Find the probability that a 0 was sent given that a 1 was received b. Find the probability that a t was sent given that a 0 was received. c. Find the total probability that a 1 was received d. Are the events that a 1 was transmitted and that a 0 was not received independent? Justify your answer.

Explanation / Answer

probabilty of 1 receipt =P(1R)=P(1S)*P(1R|1S)+P(0S)*P(1R|0S)=0.45*0.97+0.55*0.02=0.4475

a) hence probabilty that 0 was sent given 1 was in receipt =P(0S|1R)=P(0S)*P(1R|0S)/P(1R)=0.55*0.02/0.4475

=0.0246

b)probabilty that 0 was erceived =P(0R)=1-P(1R)=1-0.4475=0.5525

hence probabilty that 1 was sent given 0 was received P(1S|0R)

=P(1S)*P(0R|1S)/P(0R)=0.45*0.03/0.5525=0.0244

c)probability 1 was received =P(1R)=0.4475

d)No as P(1S|0R) is not equal to P(1S)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.