A new species of fly is found to be a carrier of a tropical disease. Experimental studies on a sample of 1000 flies have determined that 75% of males in the sample are carriers of the disease, whereas only 60% of the females are carriers of the disease. Suppose that the sample consists of 400 males and 600 females. i. What is the probability that a fly selected at random from the sample is a carrier of the disease? ii. A sequence of trials is performed where a fly is selected at random from the sample and it is recorded whether the fly is a carrier of the disease. What is the probability that in three trials at least two carriers were selected? iii. Using an appropriate approximation, estimate the probability that in 100 trials at least 60 carriers were selected. iv. What is the (conditional) probability that a fly selected at random from the sample is female, given that it is a carrier of the disease?