I am working on tsitiklis probability book. and there is this solved example in the book which i cannot understand. Please
A conservative design team, call it C, and an innovative design team, call it N, are asked to separately design a new product within a month. From past experience we know that: (a) The probability that team C is successful is 2/3. (b) The probability that team N is successful is 1/2. (c) The probability that at least one team is successful is 3/4. Assuming that exactly one successful design is produced, what is the probability that it was designed by team N?
Then it goes one and states:
There are four possible outcomes here, corresponding to the four combinations of success and failure of the two teams: SS: both succeed, FF: both fail, SF: C succeeds, N fails, FS: C fails, N succeeds.
It further states:
We were given that the probabilities of these outcomes satisfy:
P(SS) + P(SF) = 2/3 , P(SS) + P(FS) =1/2. P(SS) + P(SF) + P(FS) =3/4.
and from these relations, together with the normalization equation P(SS) + P(SF) + P(FS) + P(FF) = 1
we can obtain the probabilities of individual outcomes
P(SS)= 5/12, P(SF)=1/4, P(FS)=1/12, P(FF)=1/4.
my question is how does he do this ? and i don't get it that
P(SS) + P(SF) + P(FS) =3/4. is given ? how does he compute this ?
From the question, we can only infer that P(SF) = 2/3 and that P(FS) =1/2.
I don't get it how he infers that P(SS) + P(SF) = 2/3
Any advise ? And then i just don't get it how he computes
P(FS) = 1/12 etc...