Probability of selecting one card from a standard deck

Three probabilities from the same 52 cards. The first two are counting. The third asks for both conditions at once, and that is where the deck's structure matters.

01 Worked Example Video

▸ VIDEO COMING SOON

A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

02 Recognize the Question

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

By colour

One card is drawn from a standard deck.

What is the probability it is red? Write it as a fraction.

One rank

One card is drawn from a standard deck.

What is the probability it is an ace? Write it as a fraction.

An AND with the ace trap

One card is drawn from a standard deck.

What is the probability it is red and a face card? Write it as a fraction.

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 The Rule

52 cards = 4 suits × 13 ranks every suit-and-rank pair appears exactly once

face cards are J, Q, K — 3 per suit, 12 in all aces are not face cards

P(A and B) = count of cards that are both over 52

Because the deck holds every suit-rank combination exactly once, an “and” question is a small multiplication: 1 suit × 3 face ranks = 3 cards. You can also just find them in the table and count.

Common slips

(1) Counting the ace as a face card. It is not. Face cards are Jack, Queen and King only, so 12 in the deck rather than 16. (2) Adding for an AND. 13 + 12 counts cards that are neither, and exceeds the number that qualify. (3) Reducing when the instruction says write it as a fraction. Check what form is wanted.

04 Practice — Step by Step

Two counts, then the overlap

One card is drawn at random from a standard 52-card deck. The deck has four suits (hearts, diamonds, spades, clubs) of thirteen ranks each: ace, 2 through 10, jack, queen, king.

(a) What is the probability the card is a club?
(b) What is the probability it is a numbered card (2 through 10)?
(c) What is the probability it is a club and a numbered card?

Write your answers as fractions.

Step 1

(a) Clubs

How many clubs are in the deck, out of 52?

Step 2

(b) Numbered cards

Ranks 2 through 10 is how many ranks? Multiply by 4 suits, then put it over 52.

Step 3

(c) What does AND mean here?

You want cards that are clubs and numbered. How many?

Step 4

(c) As a fraction

9 cards out of 52.

Q19 Exam 3 Review

Probability of selecting one card from a standard deck

The AND is a rectangle, not a sum