A bag contains 2 n+1 coins. It is known that n of these coins have head on both sides whereas, the other n+1 coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is 31 42 , then the value of n is

Step-by-step solution

Given, n coins have head on both the sides and (n+1) coins are fair coins. Total coins =2 n+1 Let events E₁, E₂ be the following E₁= Event that an unfair coin is selected E₂= Event that a fair coin is selected P (E₁ )= n 2 n+1 and P (E₂ )= n+1 2 n+1 From the law of total probability, P(E)=P (E₁ ) P ( E E₁ )+P (E₂ ) P ( E E₂ ) array ll & 31 42 = n 2 n+1 1+ n+1 2 n+1 1 2 & 31 42 = 2 n+n+1 2(2 n+1) & 31 2(2 n+1)=42(3 n+1) & 124 n+62=126 n+42 & 2 n=20 & n=10 array