Question

A bag contains n + 1 coins. It is known that one of these coins

shows heads on both sides, whereas the other coins are fair. Once coin is selected at random and tossed. If the probability that toss results in heads is $\frac { 7 } { 12 }$ , then the value of n is -

• A. 3
• B. 4
• C. 5
• D. None of these

Answer 1

Answer: (C)

5

Answer 2

Let E₁, denote the event “a coin with two heads” is selected and E₂, denote the event “a fair coin is selected”. Let A be the event “the toss results in heads”. Then,

P (E₁) = $\frac { 1 } { 2 }$\ P(1) = P (E₁) P $\frac { 7 } { 12 }$= × 1 + $\frac { \mathrm { n } } { \mathrm { n } + 1 }$ × $\frac { 1 } { 2 }$ $\left[ \because \mathrm { P } ( \mathrm { A } ) = \frac { 7 } { 12 } \right]$

Ž 12 + 6n = 7n + 7 Ž n = 5.

Hence (3) is correct answer