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GATE | GATE-CS-2015 (Set 1) | Question 65
• Last Updated : 19 Feb, 2015

Consider a LAN with four nodes S1, S2, S3 and S4. 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 S1, S2, S3 and S4 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 _________.
(A) 0.462
(B) 0.711
(C) 0.5
(D) 0.652

Explanation:

```The probability of sending a frame in the first slot
without any collision by any of these four stations is
sum of following 4 probabilities

Probability that S1 sends a frame and no one else does +
Probability thatS2 sends a frame and no one else does +
Probability thatS3 sends a frame and no one else does +
Probability thatS4 sends a frame and no one else does

= 0.1 * (1 - 0.2) * (1 - 0.3) *(1 - 0.4) +
(1 -0.1) * 0.2 * (1 - 0.3) *(1 - 0.4) +
(1 -0.1) * (1 - 0.2) * 0.3 *(1 - 0.4) +
(1 -0.1) * (1 - 0.2) * (1 - 0.3) * 0.4

= 0.4404 ``` My Personal Notes arrow_drop_up
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