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 the probability of tossing a head when a coin is picked at random from a bag containing \( 2n + 1 \) coins is \( \frac{31}{42} \).

### Step-by-Step Solution:

1. **Identify the Types of Coins**:
- There are \( n \) coins with heads on both sides (unfair coins).
- There are \( n + 1 \) fair coins (one head and one tail).

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