Correct Answer - Option 2 : 0.09
The formula to calculate probability in Poisson Process is:
\(P\left( {X = x} \right) = \frac{{{{\left( {\lambda t} \right)}^x}}}{{x!}}{e^{ - \lambda t}}\)
Where:
x = number of success
t = time duration
= Average number of success during the time duration
Calculation:
Given that, In an S-ALOHA data packet transmission system,
x = experience a collision with another user = 1
t = packet duration
= 10 msec = 10 × 10-3 sec
λ = total traffic rate during packet transmission
= 10 packets/sec
\(\therefore \lambda t = 10 \times 10 \times {10^{ - 3}} = {10^{ - 1}} = 0.1\)
\(\therefore P\left( {X = 1} \right) = \frac{{{{\left( {0.1} \right)}^1}.{e^{ - 0.1}}}}{{1!}}\)
\( = \frac{{0.090}}{1} = 0.090\)