GATE 2015 CS – Question 39
Consider a LAN with four nodes $S_1, S_2, S_3$ and $S_4$. 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 $S_1, S_2, S_3$ and $S_4$ 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 ________.
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Correct answer: 0.40 to 0.46
Explanation
A frame is sent without collision only when exactly one station generates a frame in the slot. Add the probability for each station being the only one: $0.1(0.8)(0.7)(0.6) + 0.9(0.2)(0.7)(0.6) + 0.9(0.8)(0.3)(0.6) + 0.9(0.8)(0.7)(0.4) = 0.0336 + 0.0756 + 0.1296 + 0.2016 = 0.4404$. The official key accepts 0.40 to 0.46.