In a game, a man wins rupees five for a six and loses rupee one for any other number, when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.

Explanation

To find the expected value of the amount the man wins or loses in the game, we can follow these steps:

### Step 1: Define the outcomes
When a fair die is thrown, the outcomes can be categorized based on whether the man rolls a six or not. He wins Rs 5 for rolling a six and loses Rs 1 for any other number (1, 2, 3, 4, or 5).

### Step 2: Calculate the probabilities
- The probability of rolling a six (winning) is \( P(\text{6}) = \frac{1}{6} \).
- The probability of rolling any other number (losing) is \( P(\text{not 6}) = \frac{5}{6} \).
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