Exponential distribution v. Poisson?

Suppose that golfers arrive at the starter's booth of a golf course at a Poisson rate of 8 per hour. If a golfer has just arrived, what is the probability that the next golfer will arrive within twelve minutes. I first approached this using Poisson's distribution function. So 8 golfers/60 min = 0.1333 golfers/min x 12 min = 1.6 golfers/12 minute interval. Then, I plugged this into the formula. So, f(1) = [((1.6)^1)e^-1.6)]/1! and got 0.3230. Now, thinking that Poisson and the exponential distribution are related, I decided to check this result with the exponential function. BUT... 1-e(-12/7.5) = 0.7981. So which result is correct...?