7.(5pts each) Amazon customers purchase items from the website regularly. Sometimes items they are looking for are not available and sometimes the item is not offered with the Prime shipping feature. In a sample of 850 customers on their most recent purchase attempt 100 found their item not available, 200 found their item not offered with Prime shipping, and 53 reported not having either.

Item availabe A Item not availbe A^C Totals

Has Prime shipping (P) 603 47 650

Doesn't have Prime shipping (P^c) 147 53 200

Totals 750 100 850

a - What proportion of these customers found their item available or having Prime shipping?

b - What proportion of customers who found their item available did not have the option for Prime shipping?

d) Given that a customer did not have an option for Prime shipping, what is the probability that they have the item available for purchase?

e) Are the events {the item is available} and {Prime shipping is available} independent? Justify your answer using probabilities. No credit will be given without proper justification. Circle one: Yes. No