Here's an illustration , suppose I have of deck of 52 cards(well shuffled) and I pick 10 cards at random and now again I pick a card from those 10 cards,
(I)what is the probability that it's ace of diamonds?
(II)what is the probability that a cards drawn is a face card. By deck of cards I mean normal playing cards
I feel the answer should be 1/52. I have tried searching this over web but no success.
On
It is easy to see that every card has the same probability (i.e. there is symmetry). If that probability is $p$, then the probability of picking any specific card is $\frac{p}{52p}=\frac1{52}$.
The probability of drawing out an ace of diamond from those 10 cards depend on whether it is in those 10 cards or not. The probability of the ace of diamond being in the first 10 cards that were drawn is ${10\over 52}$ and probability of drawing an ace of diamond out of those 10 card is ${1\over 10}$. So in total the probability of drawing an ace of diamond is $${10\over 52}*{1\over 10}={1\over 52}$$ So yes, your answer is right. The probability is not changed, its still ${1\over 52}$. I think we can use proportion for the part ii). As saying I have got 5 marks out of 10 is equivalent to I have got 50 out of 100. Similarly there are 12 face cards in 52 cards is equivalent to we have ${30\over 13}$ face cards in those 10 cards. So the probability of choosing a face cards from those 10 cards is $${{30\over 13}\over 10} = {3\over 13}$$ The first part can be solved in the same way.