Quantum mechanics(expected probability)

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The discussion revolves around calculating the probability of a specific state A1 for the first particle in a quantum mechanics scenario involving two particles with defined states and probabilities. The user struggles with relating the composite state |C> to the individual probabilities of states A and B. They attempt to express |C> as a linear combination of the states but find it challenging to derive the original component probabilities from the resultant probability. There is a suggestion that the calculation might be simplified by summing over the probabilities of A1 combined with each state Bi. The conversation highlights the complexities of quantum probability and the need for clarity in applying quantum mechanics principles.
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Homework Statement



suppose we have two particles, first with probable states A1,A2,A3 and state B1,B2,B3 each with a certain probability P
Now if we know the probability of composite state |C> is Q
what is the probability to get the first particle to be A1?

im troubled. please help thanks

Here ,probability of getting C is any linear combination of A and B = aP(A)+bP(B)

Homework Equations





The Attempt at a Solution


i have tried to do like this
because C equals one of these 9 states (A1,A2,A3)+(B1,B2,B3)
lets call them |1>,|2>,...,|9>

i don't know how to relate use the "resultant" prbability to get back the original component probability

is it correct to use, for example <C|1> in calculation, I am in trouble
 
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You have a very fuzzy explanation of the problem, but isn't it as simple as (A1,Bi) summed over i?
 

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