I have to test whether two events are independent. I want to do this by checking whether P(A)P(B)=P(A and B), but I've been told that's not valid in the context, and I need to use P(A|B)=P(A). I don't understand why these two equations aren't equivalent statements. Context below:
"Records kept by a canteen in a business centre show that 62% of its customers work in sales. 75% of the customers who work in sales order fruit with their meal, whilst for other customers the figure is 55%.
Explain whether the records indicate that working in sales and ordering fruit with a meal are independent events."
I understand that I can check whether P(S|F)=P(S), but I don't understand why I can't check whether P(S)P(F)=P(S and F). Please help!