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Two cards are drawn from a standard deck of cards. Find each probability. $P(\text { both either black or an ace) }$

$\frac{63}{221}$

Intro Stats / AP Statistics

Algebra

Chapter 12

Probability and Statistics

Section 5

Adding Probabilities

Sampling and Data

The Normal Distribution

Introduction to Combinatorics and Probability

Oregon State University

McMaster University

Harvey Mudd College

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

02:18

Two cards are drawn from a…

01:40

00:41

A card is drawn from a sta…

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02:44

02:52

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If two cards are drawn wit…

So for this problem, if we draw two cards from the top of the deck, what are the chances of them being both either black or an ace? So this problem is actually very simple. We just were only given two terms here, so both have to be either Black Rene. So we're gonna actually multiply our two fractions together. So our first fraction are our first fraction is going to be. Well, what is the chance of drawing the first card? It's a black or an ace. Well, there's 26 black cards, and then there's too aces that are not black. So 26 plus two is going to 28/52. That's how many cards in the deck. If you've already drawn one of these cards, then there should only be 27 out of 51 cards left in the deck. So if we multiply that together, then we end up with a fraction of 756 over 2652. You write that 2652 and if you simplify that, then you should end up with the fraction of 63 over 221. That is the probability of drawing either a black or nace for both of them.

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