0
$\begingroup$

For an assignment, I have to determine the chance of drawing one queen after a set amount of cards without replacement.

The cards drawn start at 1 and go all the way up to 49 cards:

1 cards = 7.69% chance

2 cards = ____% chance

3 cards = ____% chance

...

49 cards = 100% chance

I have determined that the chance of drawing a queen is 4/52. For every card you draw, the denominator decreases by one. So the probability of drawing one queen by two cards is something along the lines of: 4/52(chance of queen) * 48/51 (chance of drawing something other than queen).

3 draws would be something like: 4/52(chance of queen) * 48/51(chance of no queen) * 47/50(chance of no queen).

The table is drawn out on my paper, and there is a pattern that I am seeing, however the percentage chance of drawing a queen is decreasing after drawing more cards. I can't figure out why. Multiplying by a fraction lower than 1 is lowering my chance of finding a queen.

But wouldn't drawing more cards INCREASE your chances of finding a queen?

I am expecting drawing 48 cards to be something like >95%, but i'm actually getting 0.01% chance. Something is wrong.

I need help understanding this. If anyone could help out, it would be greatly appreciated.

$\endgroup$
1
1
$\begingroup$

Direct approach. Calculate the probability $Q_n$ of not drawing a queen with n cards and subtract from 1. $Q_n=\frac{48}{52}\frac{47}{51}...\frac{49-n}{53-n}$ and what you want is $P_n=1-Q_n$. Notice that when $n=49$, $Q_n=0$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.