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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 probability 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 ________.
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- 10.4404
- 1.4404
- 0.4404
- None of these
Correct Option: C
P = P(S1) P(~S2) P (~S3) P(~S4) + P(~S1) P(S2) P(~S3) P(~S4) + P(~S1) P(~S2) P(S3) P(~S4) + P(~S1) P(~S2) P (~S3) P(S4)
= 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 = 0.4404.
