Question

A bag contains 16 coins of which two are counterfeit with

heads on both sides. The rest are fair coins. One is selected

at random from the bag and tossed. The probability of

getting a head is.

• A. 9/16
• B. 11/16
• C. 5/9
• D. None of these

Answer 1

Answer: (A)

9/16

Answer 2

Let A be the event of selecting a counterfeit coin and B the event of getting head. Then, Required probability

$= \mathrm { P } ( \mathrm { A } \cap \mathrm { B } ) \cup \mathrm { P } ( \overline { \mathrm { A } } \cap \mathrm { B } )$

$= \mathrm { P } ( \mathrm { A } \cap \mathrm { B } ) + \mathrm { P } ( \overline { \mathrm { A } } \cap \mathrm { B } )$

$= \mathrm { P } ( \mathrm { A } ) \mathrm { P } ( \mathrm { B } / \mathrm { A } ) + ( \overline { \mathrm { A } } ) \mathrm { P } ( \mathrm { B } / \overline { \mathrm { A } } )$

$= \frac { 2 } { 16 } \times 1 + \frac { 14 } { 16 } \times \frac { 1 } { 2 } = \frac { 9 } { 16 }$