(10 points) Suppose people are asked their preferences for Valentine's Day on whether they like receiving chocolates, going on a date, and receiving flowers . Let D be the event that people like going on a date, C be the event that people like receiving chocolates, and F be the event that people like receiving flowers. Suppose that P(D) = .6, P(C) = .7, P(F) = .55, P(DnCnF) = .35, P(DNFnCc) = .05, P(DnCn FC) = .1, and P(FnCn D") =.15. (Hint: Draw a Venn diagram. If you draw a Venn diagram, you can label the Venn diagram with the appropriate answers instead of having to write out probability statements for each part.) (a) Find P(Dn Fon Cc). (2 points) (b) Find P(Fn D'n Cc). (2 points (c) Find P(C n Fon DS). (2 points) d) Find P(CUFUD). (2 points) (e) Find P(Con Fon DS). (2 points)