Recall that the prior probabilities of no oil (none), some oil (some), and much oil (much) are:
P(none) =.7 P( some) =.2 P( much) =.1
Of 100 past sites that were drilled and produced no oil, 5 gave a medium reading. Of the 400 past sites that were drilled and produced some oil, 376 gave a medium reading. Of the 300 past sites that were drilled and produced much oil, 9 gave a medium reading. This implies that the conditional probabilities of a medium reading (medium) given no oil, some oil, and much oil are:
P( medium none) =5/ 100= .05
P( medium some) 376 /400= .94
P( medium much) 9/ 300= .03
Calculate the posterior probabilities of no, some, and much oil, given a medium reading.