DSE 2009 Prob. question...Duck, Amit sir HELP!!

[Rizwan]

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 o.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

please explain this question, not getting at all.

[Sinistral]

See here
Courtesy Amit Sir.

[Amit Goyal]

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

[Rizwan]

Thanks for the quick reply, that was of great help.
:D