4 Gamma-ray bursts (GRBs) are pulses of gamma rays lasting a few seconds, which are produced by explosions in distant galaxies. They are detected by satellites in orbit around Earth. One particular satellite detects GRBs at a constant average rate of 3.5 per week (7 days). You may assume that the detection of GRBs by this satellite may be modelled by a Poisson distribution.

1. Find the probability that the satellite detects:
   1. exactly 4 GRBs during one particular week;
   2. at least 2 GRBs on one particular day;
   3. more than 10 GRBs but fewer than 20 GRBs during the 28 days of February 2013.
2. Give one reason, apart from the constant average rate, why it is likely that the detection of GRBs by this satellite may be modelled by a Poisson distribution.
   (1 mark)