Negative Exponential Distribution

a) Shoppers enter a supermarket randomly and at a uniform average rate of 4 per minute. Show that the probability that at least one shopper enters in a period of t minutes is

1 - e^(-4t).

b) The time that passes after one shopper has entered before the next enters is denoted by T minutes. Show that T has a negative exponential distribution.

a) The probability of at least one shopper - S.

The probability of no shopper - N.

P(S) = 1 - P(N).

P(N) = Poisson with x=0.

P(S) = 1 - e^(-4t).

b) This is P(T>t) = e^(-4t). But is this **showing**??

Thanks for any advice.