Given the recent emphasis on solar energy, solar radiation has been carefully monitored at various sites in Florida. For typical July days in Tampa, 30% have total radiation of at most 5 calories, 60% have total radiation of at most 6 calories, and 100% have total radiation of at most 8 calories. A solar collector for a hot water system is to be run for six days. Find the probability that three of the days produce no more than 5 calories, one of the days produces between 5 and 6 calories, and two of the days produce between 6 and 8 calories. What assumptions are you making in order for your answer to be correct?