Drawing cards if two cards are selected from a standard deck...

Drawing Cards If two cards are selected from a standard deck of 52 cards and are not replaced after each draw, find these probabilities. $$ \begin{array}{l}{\text { a. Both are } 9 \mathrm{s} \text { . }} \\ {\text { b. Both cards are the same suit. }} \\ {\text { c. Both cards are spades. }}\end{array} $$

Transcript

00:01 Okay, we're drawing two cards from a 52 card deck, and we are not replacing them.

00:07 So given this, we first want to find the probability that both of the two cards that we draw are both nines.

00:15 Remember, we're not replacing them.

00:17 So there are four nines in a deck.

00:20 So the probability that the first card is a nine would be four over 52.

00:26 And then times the probability that the second card you draw is a nine, given that the first card, the first card you draw is a nine, which means that you only have three nines left in the deck, over 51 remaining, because you're drawing without replacement.

00:42 And so plugging this in, you get a probability of 0 .045, or 0 .45%.

00:55 Part b of this question is a little tricky, but when you think about it, it's a little bit easier.

01:00 So it's the probability that both are the same suit, but it does not specify which suit.

01:05 Remember that there are four suits in a deck of cards.

01:10 And so think about it this way.

01:14 To find this, we want to know basically this entire thing is the probability that the second card you draw is, let's say, a heart given that the first card you draw is a heart.

01:28 But it doesn't have to be a heart.

01:29 That can be the same with clubs, spades, or diamonds as well.

01:32 So first think of it as the probability that the first card you draw is of a suit.

01:42 And that's going to happen 52 out of 52 times...

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