I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!
Friday, March 31, 2006
A wedding feast
At the Miller's wedding, it was determined that 90% of the guests had chicken, 80% had peas, 70% had vanilla cake, and 60% had ice cream. No one, however, had all four items. What percentage of the guests had at least one of the two deserts?
Jan, I'm glad you like it. Please come back and try themout!
90% of the guests had chicken, 80% had peas, 70% had vanilla cake, and 60% had ice cream. No one, however, had all four items. What percentage of the guests had at least one of the two deserts?
Answer: Let C be the set of guests who had chicken, P for Peas, V for Vanilla cake and I for ice cream. Then let C' represent those who didn't have chicken and so forth. Then C' = 10%, P' = 20%, V' = 30% and I' = 40%. Because no one had all four items, the union of this set is the set of all guests. And since 10+20+30+40 = 100%, these four sets are disjoint. In particular, that means that V' and I' have no members in common, so everyone must have had at least one of the two deserts.
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I love these. Clever idea for a blog. I'll be back to find the answer. I think I know, but not ready to commit.
ReplyDeleteJan, I'm glad you like it. Please come back and try themout!
ReplyDelete90% of the guests had chicken, 80% had peas, 70% had vanilla cake, and 60% had ice cream. No one, however, had all four items. What percentage of the guests had at least one of the two deserts?
Answer: Let C be the set of guests who had chicken, P for Peas, V for Vanilla cake and I for ice cream. Then let C' represent those who didn't have chicken and so forth. Then C' = 10%, P' = 20%, V' = 30% and I' = 40%. Because no one had all four items, the union of this set is the set of all guests. And since 10+20+30+40 = 100%, these four sets are disjoint. In particular, that means that V' and I' have no members in common, so everyone must have had at least one of the two deserts.