# Probability of getting one rupee coin from bag

Problem:

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?

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 second draw
= y / (x + y) × x / (x + y – 1)
Total probability = sum of these two = x/(x + y) [after simplification].

### 7 Thoughts on “Probability of getting one rupee coin from bag”

1. atoliya on October 14, 2013 at 5:52 pm said:

it doesn’t make any differnce if we take out all the coins . the probablity will remain same , because we dont know about the withdrawled coin….:)

2. Ghanshyam Singh on March 16, 2016 at 10:42 am said:

I think the answer is incorrect because we don’t have to consider whether the first draw was 1rupee coin or 50paise coin. Answer should be (2x-1)/(x+y-1)

3. Can someone elaborate the answer? Thank you.