GATE CS 2015 Set 1 — Question 49
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Computer Networks → Medium Access & LANs → ALOHA (Pure, Slotted)
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Question
Consider a LAN with four nodes and . Time is divided into fixed-size slots, and a node can begin its transmission only at the beginning of a slot. A collision is said to have occurred if more than one node transmit in the same slot. The probabilities of generation of a frame in a time slot by and are 0.1, 0.2, 0.3 and 0.4, respectively. The probability of sending a frame in the first slot without any collision by any of these four stations is ___________.
Correct answer
0.4 to 0.46
Solution
The probability that exactly one station transmits in a given slot (no collision) is the sum of the probabilities of each station transmitting while the others do not. Let . The probability is:This value falls within the range [0.40, 0.46].
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