Bayes theorem closed

Question

The chances that doctor A will diagnose a disease X correctly is 60%. The chances that a patient will die by his treatment after correct diagnosis is 40% and the chances of death by wrong diagnosis is 70%. A patient of doctor A, who had disease X, died. The chances that his disease was diagnosed correctly is ________%.

I had solved it using Bayes theorem. and getting 66.66% but answer given is 46.15.

Comments

Required probability $=\frac{0.6*0.4}{0.6*0.4 + 0.4*0.7}$ $=\frac{0.24}{0.52}$ $=46.15 \%$

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@just_bhavana I think deno should be:- 

P(died / correct) * P(correct) + P(died / !correct) * P(!correct)

which is total probability of event died.