Each of 2 cabinets identical in appearance has 2 drawers. Cabinet A contains a silver coin in each drawer, and cabinet B contains a silver coin in one of its drawers and a gold coin in the other. A cabinet is randomly selected, one of its drawers is opened, and a silver coin is found. What is the probability that there is a silver coin in the other drawer?

Answer:The probability that there is a silver coin in the other drawer is [tex]\frac{2}{3}[/tex]Step-by-step explanation:Given : Each of 2 cabinets identical in appearance has 2 drawers. Cabinet A contains a silver coin in each drawer, and cabinet B contains a silver coin in one of its drawers and a gold coin in the other. A cabinet is randomly selected, one of its drawers is opened, and a silver coin is found. To find : What is the probability that there is a silver coin in the other drawer?Solution : Let A be the event that cabinet A is chosen.Let B be the event that cabinet B is chosenLet E be the event that silver coin is chosen.Each of 2 cabinets identical in appearance has 2 drawers.So, [tex]P(A)=P(B)=\frac{1}{2}[/tex]Cabinet A contains a silver coin in each drawer, i.e. [tex]P(E|A)=1[/tex]Cabinet B contains a silver coin in one of its drawers and a gold coin in the other,i.e. [tex]P(E|B)=\frac{1}{2}[/tex]The probability that there is a silver coin in the other drawer is given by,Applying Bayes theorem,[tex]P(A|E)=\frac{P(E|A)P(A)}{P(E|A)P(A)+P(E|B)P(B)}[/tex][tex]P(A|E)=\frac{(1)(\frac{1}{2})}{(1)(\frac{1}{2})+(\frac{1}{2})(\frac{1}{2})}[/tex][tex]P(A|E)=\frac{\frac{1}{2}}{\frac{1}{2}+\frac{1}{4}}[/tex][tex]P(A|E)=\frac{\frac{1}{2}}{\frac{3}{4}}[/tex][tex]P(A|E)=\frac{2}{3}[/tex]Therefore, the probability that there is a silver coin in the other drawer is [tex]\frac{2}{3}[/tex]