A bag contains $$2n+1$$ coins. It is known that n of these coins have a head on both sides where as the rest of the coins are fair. A coin is picked up at random form the bag and is tossed. If the probability that the results in a head is $$3142$$, then the value of n is

Question

A bag contains  $$2n+1$$ coins. It is known that n of these coins have a head on both sides where as the rest of the coins are fair. A coin is picked up at random form the bag and is tossed. If the probability that the results in a head is $$3142$$, then the value of n is

Infinity Learn · Accepted Answer

Given, n coins have head on both sides and (n+1) coins are fair coins.  Let $$E1=$$ Event that an unfair coin is selected $$E2=$$ Event that a fair coin is selected $$H=$$ Event that the toss result in a head $$P(H)=PE1$$⋅$$PH/E1+PE2$$⋅$$PH/E23142=n2n+1$$⋅$$1+n+12n+1$$⋅$$12$$ ⇒ $$n=10$$

A bag contains $(2 n + 1)$ coins. It is known that n of these coins have a head on both sides where as the rest of the coins are fair. A coin is picked up at random form the bag and is tossed. If the probability that the results in a head is $\frac{31}{42},$ then the value of n is

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A bag contains 2n+1 coins. It is known that n of these coins have a head on both sides where as the rest of the coins are fair. A coin is picked up at random form the bag and is tossed. If the probability that the results in a head is 3142, then the value of n is

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Ready to Test Your Skills?

free study material

A bag contains $(2 n + 1)$ coins. It is known that n of these coins have a head on both sides where as the rest of the coins are fair. A coin is picked up at random form the bag and is tossed. If the probability that the results in a head is $\frac{31}{42},$ then the value of n is