00:01
All right, in this problem, we're looking at probability.
00:04
We've got a deck of playing cards, which has a total of 52 cards.
00:09
So our deck of playing cards, we have total cards, 52.
00:13
And then you are given, you know, it's just a standard deck.
00:17
You've got four suits, 13 cards of an ace, a two through ten, and then the three face cards, the jack, the queen, and the king.
00:28
So we're going to randomly select two cards from the deck, and we want to know the probability that both cards are face cards.
00:37
First, when we replace the first card before selecting the second one, and then without replacement.
00:43
So if you have a deck of cards and you're going to select just throughout the whole deck, what's the probability on your first selection that you get a face card? well, there's three face cards per suit, and there are four suits, which means you have 12 face cards.
01:06
And you're choosing out of 52.
01:09
That's your total card.
01:11
So let's call our event, let's call it f, which is the probability that we choose a face card.
01:17
On our first selection, we have 12 out of 52.
01:21
That's the probability of our success of choosing a face card.
01:25
Now, we are using replacement on this part a.
01:28
So we put the face card back in, which means on our second choosing, we still have 12 face cards because we replaced it.
01:38
We still have 52 total cards.
01:41
So we go ahead and we multiply these two fractions together, and we get 144 over 2 ,704.
01:53
And then when we do that division and we round to three decimal places, we get 0 .053...