Last year, Maria sold a photo of a Canada goose to a nature magazine for $7,500, and she is keen to get some good shots again this year. She booked a spot in a hide at the edge of a lake in northeastern Manitoba for late September, the middle of the autumn migration. She believes the best shots of geese are as they land on the water with the geese coming directly toward the camera and with the sun shining out of a clear sky across the shot. The hide is on the south side of the lake, so she will need the wind coming from the south (since geese land into the wind) and either morning or evening sun. Weather records indicate that, at that time of year, the chance of the wind coming from the south is 0.56 and the chance of a clear sky is 0.64 on any particular day.

a) What is the probability that Maria will have the conditions she wants on her first day in the hide? State your assumptions clearly and comment on whether you think the assumptions are true.

b) Maria booked four days in the hide. What is the probability that she will get the conditions she wants on all four days? State your assumptions clearly and comment on whether you think the assumptions are valid.