Question

There are 3 boxes each having two drawers The first box contains a gold coin in each drawer. The second, a gold coin in one drawer and a silver coin in the other. The third box contains a silver coin in each drawer. A box is chosen at random and a drawer is opened. If a gold coin is found in that drawer, then the probability that the other drawer also contains a gold coin is

• A. $\frac{1}{3}$
• B. $\frac{2}{5}$
• C. $\frac{2}{3}$
• D. $\frac{3}{5}$

Answer 1

The correct option is C $\frac{2}{3}$

if boxes are $B_{1,}{B}_{2,}{B}_{3,}P\left(B_{i,}\right)=1/3fori=1,2,3$

$P\left(\frac{G}{B_1}\right)=1,P\left(\frac{G}{B_2}\right)=1/2,P\left(\frac{G}{B_3}\right)=0$

by Baye's theorem

$P\left(\frac{B_1}{G}\right)=\frac{1\times 1/3}{1\times 1/3+1/2\times 1/3+0}=2/3$