Define events:
John will choose Physics = "P"
John will choose Chemistry = "C"
John will choose Biology = "B"
Let probability of event A = "P(A)", and "A^c" is complement of set A.
Conditional probability
"P(B|P)=P(P\\cap B)\/P(P)=0.75,\\\\\n\\ P(P\\cap B)=0.75\\cdot0.4=0.3"
"P(P|B^c)=P(P\\cap B^c)\/P(B^c)=0.05, \\\\\nP(P\\cap B^c)=0.05\\cdot(1-0.6)=0.05\\cdot0.4=0.02"
But
"(P\\cap B)\\cup (P\\cap B^c)=P\\cap(B\\cup B^c)=P\\ and \\ (P\\cap B)\\cap(P\\cap B^c)=\\empty"
Therefore "P(P)=P(P\\cap B)+P(P\\cap B^c)=0.3+0.02=0.32\\ne 0.4"
and problem conditions contradict each other, hence problem has no solution.
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