A pet shop is overstocked with budgerigars [also known as Australian parakeets or "budgies\"}, and so they plan a weekend discount sale. The budgies are available in both green and blue and there are, of course, males and females. The breakdown of colour and gender for their initial stock of 30 birds is: Blue Green Male 4 13 Female 8 5 The sale was a success, 24 of the birds being sold. Assume colour and gender preferences among the customers were entirely random, so that each bird is equally likely to have been chosen for purchase. a) Calculate the probability that the 6 unsold budgies include at least one female and at least one blue bird b) How many blue females should be expected to be among the unsold 6 birds? What is the standard deviation ofthe number of unsold blue females? c) It is discovered that none ofthe unsold birds are blue females! Does this call into question the initial assumption about customer preferences? Briefly justify your