DSE 2009 doubt Q17(part 2)

[bhavya jain]

plz help me to solve this question-
17) Jai and Vijay are taking a exam in statistics. The exam has only three grades A, B and C. The probability that Jai gets a B is 0.3, the probability that Vijay gets a B is 0.4, the probability that neither gets an A, but at least one gets a B is 0.1. What is the probability that neither gets a C but at least one gets a B?
a) 0.1 b) 0.6  c) 0.8 d) Insufficient data to answer the question

[ViV]

In what follows, I am going to write Jai's grade first followed by Vijay's grade. For example if i mention the sample point AB that would mean that Jai's grade is A and Vijay's grade is B.
Pr(Jai gets a B) = Pr(BA, BB, BC) = Pr(BA) + Pr(BB) + Pr(BC) = 0.3 ---(1)
Pr(Vijay gets a B) = Pr(AB, BB, CB) = Pr(AB) + Pr(BB) + Pr(CB) = 0.4 ---(2)
Pr(Neither gets an A, but at least one gets a B)
= Pr(BC, BB, CB) = Pr(BC) + Pr(BB) + Pr(CB) = 0.1 ---(3)
Pr(Neither gets an C, but at least one gets a B) = Pr(BA, BB, AB) = Pr(BA) + Pr(BB) + Pr(AB) = 0.6 (Add (1) and (2) and then subtract (3) from it)

Courtesy: Amit Sir!

[mrittik]

what is the difference b/w Pr(BA) & Pr(AB)? plz explain ViV....

[Dreyfus]

@Mritik....Pr(AB) is the joint prob that Jay gets A grade while Vijay gets B grade.
Similarly Pr(BA) is the joint probability that Jay gets B grade while Vijay gets A grade.

[ViV]

Right!! Vaibhav