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# Puzzle #25: Probability of getting One Rupee Coin from Bag Puzzle | Infosys

**A bag contains (x) one rupee coins and (y) 50 paise coins. One coin is taken from the bag and put away. If a coin is now taken at random from the bag, what is the probability that it is a one rupee coin?**

**Puzzle Solution:**

**Case I:** Let the first coin removed be one rupee coin One rupee coins left = (x – 1) Fifty paise coins left = y. Probability of getting a one rupee coin in the first and second draw = x/(x + y) × (x – 1)/(x – 1 + y)

**Case II:** Let the first coin removed be fifty paise coin One rupee coins left = x Fifty paise coins left = y – 1. Probability of getting a fifty paise coin in the first and one rupee coin in the second draw

= y / (x + y) × x / (x + y – 1)

Total probability = sum of these two = x/(x + y) [after simplification].

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