probability problem please help

[th3plan]

A college use two different textbooks during the last semester. During last semester 0.7 students used the text book by Professor B. and 0.3 students use the textbook by professor P. A survey at the end of the last semester showed that 0.4 of students who used Professor B. book were satisfied and 0.8 of students who used Professor P. were satisfied. If a student randomly selected and claims to have been satisfied with the text, what is the probability the student used Professor P. class ?


P(ProfP)=0.3

P(Satisfied/ProfP)=0.8

P(Satisfied and ProfP) = 0.3 * 0.8 = 0.24


Is this correct what i did ? If not can you tell me what to do, cause it just seems to straightforward and i must be missing something

[bholland]

A college use two different textbooks during the last semester. During last semester 0.7 students used the text book by Professor B. and 0.3 students use the textbook by professor P. A survey at the end of the last semester showed that 0.4 of students who used Professor B. book were satisfied and 0.8 of students who used Professor P. were satisfied. If a student randomly selected and claims to have been satisfied with the text, what is the probability the student used Professor P. class ?


P(ProfP)=0.3

P(Satisfied/ProfP)=0.8

P(Satisfied and ProfP) = 0.3 * 0.8 = 0.24


That's the probability that a student has P's textbook and was satisfied, but that isn't the probability that a student that is chosen who is satisfied is using P's textbook, they're different.

You want the conditional probability, given that he is satisfied, that he used P's book.

P(P|S) = P(PintersectS) / P(S)
P(P) = .3
P(S) = .8
P(PintersectS)=.3*.8 = .24

.24 / .8 = .30

I think.

[th3plan]

umm im not sure

[th3plan]

P(B)= 0.7
P(P)=0.3
P(S|B)=0.4
P(S|P)=0.8

P(P|S)=?

In order to find P(P|S) i apply bayes theorem (not sure)

P(P|S)=(P(P)*P(S|P))/(P(B)*P(S|B))+(P(...

P(P|S)=(0.3*0.8)/(0.7*0.4)+(0.3*0.8) =0.461538

P(P|S)=0.461538

maybe this is correct ?

[bholland]

YEah thats right