Question

When randomly choosing two cards from a standard deck of cards without replacement, what is the probability of choosing a queen and then a king?

Answer 1

Well, these events are independent of each other, so we can just find the probabilities individually, then multiply them together.

So, what is the probability of choosing a queen?

There are 4 queens out of a total of 52 cards, so it is simply `4/52`

or `1/13`

Now we find the probability of choosing a king

Remember, there is no replacement, so now we have 51 total cards because we removed a queen.

There are still 4 kings in the deck, so our probability is `4/51`

Now we found both components, just multiply them together

`1/13 * 4/51 = 4/663`

We cannot simplify further, so we are done,.