1. Recall a French roulette wheel has 18/37 red slots, and  imagine that a Nepalese  roulette wheel has 8/37 red slots.  You wish to determine whether certain Roulette data was produced by a Nepalese or French roulette wheel.  Before seeing the data, you believe that the wheel is twice as  likely to be a French wheel than  a Nepalese  wheel.  You are told that this roulette wheel came up red 7 times  in 40 spins.  After seeing this data, with what probability should you now believe that the wheel is Nepalese ?

2.  Every morning before sending my son to daycare my wife and I realize that we have forgotten to pack him a snack!  2/3rds of  the time my wife rushes off to pack him a snack and the remaining 1/3rd of the time I do.  We always pack him 10 grapes in a little  paper bag. My wife always packs him 5 green and 5 red grapes.  I don't think he likes red grapes, so I give him 9 green and only 1 red grape.  My day care provider thinks the situation is rather funny and always comments to when I pick him up in the afternoon either: 

"Oh I saw you packed Max's snack today, we all shared that lovely red grape!" 

or 

"Oh I saw your wife packed Max's snack today, thank her for all those yummy red grapes!"

Today however she had fed Max 3 green grapes from the bag, when Stephanie found the  bag and ate all the remaining grapes.    The day care provider decided that she did not want to admit to me  that Max's snack was devoured by another child, so she decides to guess who pack the snack and fortunately she knows Bayes' Theorem. 

What is an accurate estimate of the probability  that I  packed Max's snack that morning? 


.