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Mud Flaps and Elvis Cologne

Here's an interesting probability problem:

At a Christmas party Spike, Spud, and Sparky have three gifts to choose from. Two of the gifts are Yosemite Sam mud flaps and one is a bottle of Elvis Presley cologne. Spike really wants the cologne, Sparky wants the mud flaps, and Spud doesn't care what he gets. Spike knows Sparky wants the mud flaps and he also knows that Sparky helped wrap the gifts so he knows which ones have the mud flaps. Spike chooses his gift first, then Sparky chooses his and Spud gets the last one left. Just as they are getting ready to open the gifts, Spike has a brain tornado and asks to swap gifts with Spud. He thinks there is a higher probability that Spud has the gift with the Elvis cologne. Is he right?

And here's the answer:

At the last moment Spike realized that if his initial pick was mud flaps then Sparky picked the other set of mud flaps and Spud ended up with the cologne. This was the most likely scenario since Spike had a \(2/3\) probability of initially picking mud flaps and only a \(1/3\) probability of initially picking the cologne. It was therefore twice as likely that Spud had the cologne and not him. Asking Spud to switch gifts is the smart thing to do.

This problem is one of over 200 in our new book: Probability Problems and Solutions.

© 2010-2013 Stefan Hollos and Richard Hollos

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