What's the probability of third coin being of 50 cent?

Question

I was asked this question in an interview for Data Scientist position: I have 1 coin of say 10p,20p and 50p each in my pocket. I then draw out of my pocket the coin of 10p. So now I'm left with 1 coin of 20p and 50p each. Call this the 'FIRST' attempt. What is probability of getting the 50p coin in the 'THIRD' attempt?

When I said the answer is 50%, the interview told me it's a wrong answer. Is there some hidden logic to it that I'm not able to pick?

EDIT: When I mentioned 'Third' attempt, the 10p coin is not placed back in the pocket.

Answer 1

A priori, the probabbility that the third coin is 50p is $\frac 13$. But given that the first coin is 10p, the probabbility that the third coin is 50p is $\frac12$.

Answer 2

Answer:

$$P(\text{It is 50p coin in the third draw}/\text{First draw is 10p coin}) $$$$=\frac{P(\text{(50p coin in the third draw)}\cap\text{(First is 10p coin)})}{P(\text{First is 10p Coin})}$$

Total possibilities:$\text{ {10,20,50},{10,50,20}.{20,10,50}{20,50,10}{50,10,20}{50,20,10}}$.

Of these the numerator reduces to $\text{{10,20,50}}$ and the probability of the numerator is $\frac{1}{6}$ and the denominaotor reduces to $\text{{10,20,50} and {10,50,20}}$ giving the probability $\frac{1}{3}$.

Thus the required probability using Bayes' theorem is $$\dfrac{\left(\frac{1}{6}\right)}{\left(\frac{1}{3}\right)} = \frac{1}{2}$$

Thanks

Satish

Answer 3

If 50% is wrong answer. Then I think we can identify the coin by touch. Then it is not random selection.

NOTE: It is a question in Interview.