Through a routine water quality analysis, it is found that somebody has illegally dumped paint in the river. this paint has been found downstream of an area with 50 houses. this means that any of these 50 houses could have polluted the water. through analyzing the houses, a consultant has determined that there is an 90% chance that the paint used by household a is the paint that is found in the water. does this mean that there is an 90% chance that household a is guilty of polluting the stream? if yes, explain your reasoning. if not, calculate the chance that the household is guilty, and explain your reasoning. the council decides to perform a water quality check every day. this test costs $500 each day. if a pollutant is found in the water, they assume that they will find the pollutor, and they will fine them $50,000. what does the probability to find a pollutant in the sample each day at least have to be, for the council to be 90% sure that they will not lose money on these tests, in a non-leap year? the council is contemplating organizing nature walks along the river with a paid guide. the walks last for a day, and the guide charges $50 per customer per day. the salary of the guide is $1100 per week, and he is expected to guide at least 25 people per week. how certain can the council be that they will be cash-flow positive any random week?