MY END OF SEMESTER CHALLENGE

The problem below combines all kinds of probability related issues: Normal, binomial and hypergeometric distributions, conditional probabilities and lots of random variables. 

Time permitting I have used the big problem below to give my students a last challenge before the semester is over. At the undergraduate level (Business Statistics I) I usually let the whole class work together on this for an entire class period and encourage them all to bring their laptops as well as using the white board to collect the results. For my MBA stats class I have given it as a take home problem. I won't post the solution here, but if you email me (grzimek(AT)yahoo.com) and provide the URL to your faculty page (to ensure I don't send the solution to your students), I will email you the answer.

Here is the final challenge for the semester…

·                     In Aismyfavoritegradia you pass by a casino where you are asked to draw 4 cards randomly out of a poker deck (of 52 cards). The random variable W is the number of face cards in your draw (face cards being Kings, Queens and Jacks).

·                     Next you come to your favorite beer garden. You have invited 3 friends to meet you there and, even though each of them said that he would come, there is only an independent 60% chance for each of them showing up. The number of friends that show up is the random variable X

·                     Next you go to the Miller residence where two of your friends live. Jim is at home 60% of the time. If Jim is home, Joe is home with a 50% chance. If Jim is not at home, Joe is at home with a 75% chance. Denote the number of friends you meet at home as the random variable Y.

·                     Finally you run into me. I on 8 statistics books, 5 of which I have read. You have read 3 of the 8 (and those are independent of the ones I have read). We compare our reading experience and the number of books that  both of us have read is the random variable Z.

·                     Tired of all these statistics questions you decide to leave this exhausting country. At the border you run into an elf that tells you the following: Let A = max(W,X) and B = max(Y,Z). You get a random exit price which is normally distributed with mean $5,000 + $10,000*A and standard deviation $5000+$5000*B. What is the probability that the random exit price is more than $35,000?