Measurement problem quantum mechanics

Ashish Somwanshi
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Homework Statement
Suppose there are two quantum mechanical observables c and d represented by operators C and D respectively. Both operators have two eigenstates, ϕ1 and ϕ2 for C and ψ1 and ψ2 for D. Furthermore , the two sets of eigenstates are related to each other as below

ϕ1=1/13(5ψ1+12ψ2)
ϕ2=1/13(12ψ1−5ψ2)

The system was found to be in state ϕ1 initially.

If we measure D, what is the probability of finding the system in ψ2?
Relevant Equations
Born rule?
Is the answer 0.748?
 
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