A ladies’ boutique decides to offer specialised outfits for school formals. The shop has two members of staff, so they can serve up to 16 customers a day.Based on their past experience there is a 50% chance that a customer will buy adress, a 30% chance they will buy a skirt and a 20% chance they will buytrousers.If they buy a dress then there is 45% chance it will be red, 35% it will be black,otherwise they will choose a white one. If they buy a skirt there is a 50% chanceit will be black, a 30% chance it will be red, otherwise they will choose a whiteone. If they choose to buy trousers there is a 70%chance they will be black, 20%chance they will be white, otherwise they will be red. If they need a blouse thereis a 35% chance it will be black, otherwise it will be white. If the top of the outfitis black then there is a 70% chance they will choose black shoes, but if the top isnot black then they will only choose black shoes 60% of the time.
a) What is the probability that the first customer will choose an outfit that is all one colour?
b) If the first customer chooses a black blouse, what is theprobability that the next customer will purchase an outfit with ablack blouse as well?
c) If the first customer chooses a pair of white shoes, what is the probability that her outfit has a white top?
d) If they are expecting about 80 customers in total, how would you recommend they stock the shop? State any assumptions andconditions that you apply.