Originally Posted by

**MathBlaster47** Just making sure I have my head on straight when it comes to the whole probability thing.

One card is drawn from a deck of 52. What is the probability that it is:

(a): A diamond?

(b):A King?

(c):An Ace or King?

Working:

(a):There are $\displaystyle _{52}C_1$ or $\displaystyle \frac{52!}{1!51!}=52$ ways of picking a card, and there are 13 diamond cards so there are $\displaystyle _{13}C_1$ or $\displaystyle \frac{13!}{1!12!}=13$ ways of picking a diamond. So there the probability of drawing a diamond card is $\displaystyle \frac{13}{52}=\frac{1}{4}$.

(b):There are $\displaystyle _{52}C_1$ or $\displaystyle \frac{52!}{1!51!}=52$ ways of picking a card, and there are 4 Kings so there are $\displaystyle _4K_1$ or $\displaystyle \frac{4!}{1!3!}=4$ ways to draw a king. So the probability of drawing a King is$\displaystyle \frac{4}{52}=\frac{1}{13}$.

(c):There are $\displaystyle _{52}C_1$ or $\displaystyle \frac{52!}{1!51!}=52$ ways of picking a card, there are 4 Aces and 4 Kings so there are 8 cards to choose from so, there are $\displaystyle _8A_1$ or \frac{8!}{1!7!}=8 ways to draw either of the cards.

Therefore, the probability of drawing either an Ace or King is $\displaystyle \frac{8}{52}=\frac{2}{13}$

Am I doing it right?