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

\(\therefore \lambda t = 10 \times 10 \times {10^{ - 3}} = {10^{ - 1}} = 0.1\)

\(\therefore P\left( {X = 1} \right) = \frac{{{{\left( {0.1} \right)}^1}.{e^{ - 0.1}}}}{{1!}}\)

\( = \frac{{0.090}}{1} = 0.090\)