In a large local-area-network (LAN), a message is successfully transmitted if it

Question

In a large local-area-network (LAN), a message is successfully transmitted if it does not encounter any “collisions”. These collisions are due to other users trying to transmit messages at the same time. If a collision occurs another transmission is attempted at a later time. These attempts continue until the message is successfully transmitted without any collisions. Whenever a message transmission is attempted, the probability of collision is 90%.

(a) What is the probability that a certain message is transmitted at exactly the 3rd attempt?

(b) What is the probability that it would take a total of exactly 5 attempts to transmit 3 messages?

Explanation / Answer

(a) Cetain message is transmitted at exactly the 3rd attempt that means earlier two attempts will be interreupted by collison and in third attempt there will be no collision.

Pr( success) = 0.1

Pr( Collision or failure) = 0.9

Pr ( X = 3 attempt) = (0.9)2 * 0.1 = 0.081

(b) Pr( 3 transmission in exactly 5 attempts) = in earlier 4 attempts there are 2 transmission and in last attempt there is a transmission .

Pr( 3 out of exactly 5) = 4C2 (0.1)2 (0.9)2 * (0.1) = 0.00486

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

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