Probability of picking a specific card from a deck of X cards after N draws without replacement.

Question

What the title says, what method would I use to calculate the above. To give an example, imagine I wanted to pick the queen of hearts, that specific card, out of a deck of 52 cards. How would I calculate the probability after, say, 20 draws? (without replacement)

Answer 1

All draws are equally likely to show the Queen of Hearts

• so the probability of picking it on the $20$th draw is $\frac{1}{52}$

• and the probability of picking it in the first $20$th draws without replacement is $\frac{20}{52}$

You can do an induction proof if necessary but I do not think it is.