H1 = { we know the answer }
H2 = { we don't know the answer and will flip a fair coin }
A ={ choosing the correct answer }
a) By the formula of total probability , we have
"P(A) = \\sum P(H_i)*P(A|H_i)"
So P(A) = 0.7 * 1 + 0.3 * 0.5 = 0.85
Answer 1): 0.85
b) By formula of Bayes:
"P(H_i|A) = P(A*H_i)\/P(A)= P(A|H_i)*P(H_i)\/P(A)"
So for second question we have to find "P(H_1|A)" :
"P(H_1|A) = P(A|H_1)*P(H_1)\/P(A) =\n 1* 0.7 \/ 0.85 = 0.823529..."
Answer 2) 0.823529...
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