Question

If a box contains 19 unbiased coins and 1 biased coin with both faces head. If a coin is randomly chosen out of this box and tossed. If the head appears, then the probability that the biased coin was selected

(1) \(\frac{19}{21}\)

(2) \(\frac{1}{3}\)

(3) \(\frac{1}{5}\)

(4) \(\frac{1}{6}\)

Answer 1

Correct option is: (1) \(\frac{19}{21}\)    

\(P\left(\frac{u}{H}\right)=\frac{P(u) P\left(\frac{H}{u}\right)}{P(u) P\left(\frac{H}{u}\right)+P(\bar{u}) P\left(\frac{H}{\bar{u}}\right)}\)

\(=\frac{\frac{1}{20} \times 1}{\frac{1}{20} \times 1+\frac{19}{20} \times \frac{1}{2}}=\frac{2}{2+19}=\frac{2}{21}\)