A bag contains `(2n+1)` coins. It is known that `n` of these coins have a head on both sides whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is `(31)/(42)` , determine the value of `n` .

Explanation

To solve the problem, we need to find the value of \( n \) given that a bag contains \( 2n + 1 \) coins, where \( n \) coins have heads on both sides and the remaining \( n + 1 \) coins are fair. The probability of tossing a head is given as \( \frac{31}{42} \).

### Step-by-Step Solution:

1. **Identify the Total Number of Coins**:
The total number of coins in the bag is \( 2n + 1 \).

2. **Determine the Types of Coins**:
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