The Sturt Stony Desert is a \"gibber\" desert partly located in south-western Queens- land (Australia) with an estimated area of 29750 km2. Suppose that you happen to be camping with friends and want to take a picture of the fattailed dunnart (Sminthopsis crassicaudata). One of your friends claims that its appearance in this area follows a spatial Poisson process with constant rate 0.5 per km2. You'd re ally like to capture a spectacular photo of this unusual desert creature, but before setting out you want to make sure you have a reasonable chance of success if your friend's claim is correct. You and your friend can carry enough water and food as well as your photographic gear to scour a 0.25 km2 area before you have to return to camp. (a) If your friend is correct, what is the probability that you would see at least one fattailed dunnart on a single trip? [1] (b) How many trips (visiting distinct areas) should you expect to take before you have 6 sightings of the fattailed dunnart? [1] (c) Suppose a recent survey of put the total population of the fattailed dunnart in the Sturt Stony Desert at 5 x 105. Given this information, what is the conditional probability that you would see at least one fat-tailed dunnart on a single trip? [1]