Probability of selecting one card from a standard deck

Three-part: a simple count for face cards, another simple count for red cards, then the addition rule for face-or-red with the six-card overlap correction.

01 Mini-Lesson 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 What This Looks Like on ALEKS

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

Face / red / face or red v1

Suppose one card is drawn at random from a standard deck of 52 cards. Find:

(a) P(face card)
(b) P(red card)
(c) P(face card OR red card)

Write each answer as a fraction.

King / spade / king or spade v2

One card is drawn from a 52-card deck. Find P(king), P(spade), and P(king or spade). Write each as a fraction in lowest terms.

Ace / heart / ace or heart v3

One card is drawn from a 52-card deck. Find P(ace), P(heart), and P(ace or heart). Write each as a fraction in lowest terms.

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 How to Solve It

P(A or B) = P(A) + P(B) − P(A and B)
subtract the overlap once so it isn't counted twice

The addition rule. Subtract P(A and B) to avoid double-counting the cards in both sets.

(a) P(face card).

Face cards are J, Q, K in each of 4 suits: 3 × 4 = 12 face cards.

P(face) = 12/52 = 3/13

(b) P(red card).

Hearts and diamonds are red: 2 suits × 13 cards = 26 red cards.

P(red) = 26/52 = 1/2

(c) P(face OR red) — addition rule.

Identify the overlap: cards that are both face AND red are the J/Q/K of hearts and diamonds — 6 cards. So P(face AND red) = 6/52.

P(face or red) = 12/52 + 26/52 - 6/52 = 32/52 = 8/13

▸ COMMON SLIPS(1) Skipped the overlap subtraction. 12/52 + 26/52 = 38/52 counts the six red face cards twice. Subtract 6/52 once to get 32/52. (2) Confused face with picture card. Face cards = J, Q, K only (12 total). The ace is not a face card in standard usage. (3) Forgot to reduce. 12/52 → 3/13. 32/52 → 8/13. ALEKS expects lowest terms.

04 Practice — Step by Step

Try the king-or-spade variant. Same recipe: count each set, count the overlap (just one card here), apply the rule.

P(king or spade).

One card drawn from a standard 52-card deck. What is P(king or spade)? Fraction in lowest terms.

P =

▸ NICE WORK

You've walked through the whole problem.

That's the move. ALEKS will give you a different version with different numbers — but the steps are the same.

Q2 Q4