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Consider a LAN with five nodes. Time is divided into fixed-size slots. A node can begin its transmission only at the beginning of a slot. A collision occurs if more than two nodes transmits in the same slot. The probabilities of generation of a frame in a time slot by these LAN are 0.2, 0.3, 0.25, 0.16 and 0.09, respectively. The probability of transmission in the first slot without any collision by any of these five stations is _________. (Compute the answer up to 2 decimal places.)
    Correct answer is between '0.41,0.42'. Can you explain this answer?
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    Consider a LAN with five nodes. Time is divided into fixed-size slots....
    Probability of transmission on the first slot by 1st node:
    = 0.2 × (1 – 0.3) × (1 – 0.25) × (1 – 0.16) × (1 – 0.09)
    = 0.2 × 0.7 × 0. 75 × 0.84 × 0.91
     
    Probability of transmission on the first slot by 2nd node:
    = (1 - 0.2) × 0.3 × (1 – 0.25) × (1 – 0.16) × (1 – 0.09)
    = 0.8 × 0.3 × 0. 75 × 0.84 × 0.91
     
    Probability of transmission on the first slot by 3rd node:
    = (1 - 0.2) × (1 - 0.3) × 0.25 × (1 – 0.16) × (1 – 0.09)
    = 0.8 × 0.7 × 0.25 × 0.84 × 0.91
     
    Probability of transmission on the first slot by 4th node:
    = (1 - 0.2) × (1 - 0.3) × (1 - 0.25) × 0.16 × (1 – 0.09)
    = 0.8 × 0.7 × 0.75 × 0.16 × 0.91
     
    Probability of transmission on the first slot by 5th node:
    = (1 - 0.2) × (1 - 0.3) × (1 - 0.25) × (1 - 0.16) × 0.09
    = 0.8 × 0.7 × 0.75 × 0.84 × 0.09
     
    Probability = 0.080262 + 0.137592 + 0.107016 + 0.061152 + 0.031752 = 0.4177
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    Consider a LAN with five nodes. Time is divided into fixed-size slots....
    Understanding the Problem
    In a LAN with five nodes, each node has a specific probability of generating a frame in a time slot. A collision occurs if more than two nodes attempt to transmit simultaneously. We are tasked with calculating the probability of successful transmission without collision.
    Node Probabilities
    - Node 1: 0.2
    - Node 2: 0.3
    - Node 3: 0.25
    - Node 4: 0.16
    - Node 5: 0.09
    Calculating the Probability of No Collision
    To find the probability of transmission without a collision, we consider the following scenarios:
    1. Only One Node Transmits:
    - The probability that exactly one of the nodes transmits can be calculated by summing the probabilities of each node transmitting while the others do not.
    2. Probability of No Transmission:
    - The probability that a node does not transmit is given by (1 - probability of transmission).
    Calculating Individual Probabilities
    - For each node i (i = 1 to 5), the probability of it transmitting while the others do not is:
    - Node 1: 0.2 * (1 - 0.3) * (1 - 0.25) * (1 - 0.16) * (1 - 0.09)
    - Node 2: 0.3 * (1 - 0.2) * (1 - 0.25) * (1 - 0.16) * (1 - 0.09)
    - Node 3: 0.25 * (1 - 0.2) * (1 - 0.3) * (1 - 0.16) * (1 - 0.09)
    - Node 4: 0.16 * (1 - 0.2) * (1 - 0.3) * (1 - 0.25) * (1 - 0.09)
    - Node 5: 0.09 * (1 - 0.2) * (1 - 0.3) * (1 - 0.25) * (1 - 0.16)
    Final Probability Calculation
    1. Calculate the probabilities for each node.
    2. Sum these probabilities to get the total probability of transmission without collision.
    After performing the calculations, the final result is approximately 0.41.
    Thus, the probability of transmission in the first slot without any collision by any of these five stations is between 0.41 and 0.42.
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    Consider a LAN with five nodes. Time is divided into fixed-size slots. A node can begin its transmission only at the beginning of a slot. A collision occurs if more than two nodes transmits in the same slot. The probabilities of generation of a frame in a time slot by these LAN are 0.2, 0.3, 0.25, 0.16 and 0.09, respectively. The probability of transmission in the first slot without any collision by any of these five stations is _________. (Compute the answer up to 2 decimal places.)Correct answer is between '0.41,0.42'. Can you explain this answer?
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    Consider a LAN with five nodes. Time is divided into fixed-size slots. A node can begin its transmission only at the beginning of a slot. A collision occurs if more than two nodes transmits in the same slot. The probabilities of generation of a frame in a time slot by these LAN are 0.2, 0.3, 0.25, 0.16 and 0.09, respectively. The probability of transmission in the first slot without any collision by any of these five stations is _________. (Compute the answer up to 2 decimal places.)Correct answer is between '0.41,0.42'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider a LAN with five nodes. Time is divided into fixed-size slots. A node can begin its transmission only at the beginning of a slot. A collision occurs if more than two nodes transmits in the same slot. The probabilities of generation of a frame in a time slot by these LAN are 0.2, 0.3, 0.25, 0.16 and 0.09, respectively. The probability of transmission in the first slot without any collision by any of these five stations is _________. (Compute the answer up to 2 decimal places.)Correct answer is between '0.41,0.42'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a LAN with five nodes. Time is divided into fixed-size slots. A node can begin its transmission only at the beginning of a slot. A collision occurs if more than two nodes transmits in the same slot. The probabilities of generation of a frame in a time slot by these LAN are 0.2, 0.3, 0.25, 0.16 and 0.09, respectively. The probability of transmission in the first slot without any collision by any of these five stations is _________. (Compute the answer up to 2 decimal places.)Correct answer is between '0.41,0.42'. Can you explain this answer?.
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