Date: Fri, 27 Mar 1998 17:55:09 -0500

From: Alex Bogomolny

Dear James:

All the wording of your problem is not essential.

An event happens with the probability 1/4. Assuming independent trials, what is the probability that the event will happen twice?

Answer: 1/4 times 1/4 = 1/16.

Your problem is somewhat ambiguous. And I would, perhaps, request of the teacher a little more thoughtfulness. If, for example, during a day your fellow never touches the keys after putting them into his pocket, you may safely assume that if a loss occurs, the whole content of the pocket (two sets of keys included) will be lost in one trial. In order to apply my approach events must repeatedly happen that may lead to key loss and one item loss must be independent of the other. This does not follow from your formulation.

Best regards,

Alexander Bogomolny