Question

In P-persistent CSMA network there are 5 systems in a slot. The probability of station not transmitting the data is 0.6. Only two stations should transmit the data to avoid collision. What is the probability that channel is collision free?

My answer is 0.6825 and answer given is 0.34 - 0.35.

I solved this as P (no collision) = either 2 stations are transmitting or 1 station or none.

Answer 1

Favorable case here is no station is transmitting, exactly one is transmitting or exactly 2 is transmitting.

$P = {}^5C_0 \times {0.6}^5 + {}^5C_1 \times {0.6}^4{0.4} + {}^5C_2 \times {0.6}^3{0.4}^2
\\= 0.68256.$

Comments

Is this ans correct or 0.365 if we will take on 5C2 case???

Can u clarify?

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Why would there be any collision in the case of only one station transmitting? Makes perfect sense to include 5C0 and 5C1.

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Sir,jab only 2 stations should send frame likha hua hai,to ham 0,1 station ki probability  kyu le????

Answer 2

In question ask only two stations transmit. So, we consider two stations only.

probability =5C2(0.4²⁾(0.6³)=0.3456

Comments

but of only one statuon transmit then also it will be collisoin free. why we are not considering that case?