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Probability practice

Playing card probability worksheets

Calculate probabilities in a standard 52-card deck. Choose single draws or independent draws with replacement, with explicit card conventions and an explained answer key.

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Use a standard 52-card deck without jokers. For multiple draws, replace the card and shuffle before the next draw. Follow the stated order and card conditions.

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State what happens between draws

Use a standard 52-card deck without jokers. Single-draw questions count the cards satisfying an event. The two-draw questions replace and shuffle the first card, making the second draw independent.

Face cards mean J, Q and K. An ace is a separate rank. Read and/or conditions carefully: an overlapping card belongs only once in a union.

Learning objective

What this activity builds

Count card events accurately and multiply probabilities for ordered independent draws with replacement.

Worked example

Draw a heart, replace it and shuffle, then draw an ace. What is the probability of this ordered event?

(13/52) × (4/52) = 1/52.

Thirteen cards are hearts, and four cards are aces. Replacing the first card restores all 52 cards, so the second draw is independent. There are 13 × 4 favorable ordered pairs among 52 × 52 possible pairs.

Teaching notes

Make the practice count

  • Review that J, Q and K are face cards; an ace is not a face card.
  • Use the words and, or, first and then precisely.
  • For a union, count an overlapping card only once.
  • Model replacement physically before multiplying fractions.

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Uses a standard 52-card deck without jokers. Multi-draw questions replace and shuffle the first card before the second draw.

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Math SheetNameScore/ 10TeacherDatePlaying Card ProbabilityUse the stated equally likely outcomes. Give each probability as a simplified fraction.1.A–KDraw a card, replace it, shuffle, and drawagain from a standard 52-card deck withno jokers. Face cards are J, Q, and K; anace is separate; numeric ranks are2–10.What is the probability of draw 1: 6 and draw 2: J?2.A–KDraw one card from a well-shuffledstandard 52-card deck with no jokers.Face cards are J, Q, and K; an ace isseparate; numeric ranks are 2–10.What is the probability of K?3.A–KDraw one card from a well-shuffledstandard 52-card deck with no jokers.Face cards are J, Q, and K; an ace isseparate; numeric ranks are 2–10.What is the probability of face card?4.A–KDraw one card from a well-shuffledstandard 52-card deck with no jokers.Face cards are J, Q, and K; an ace isseparate; numeric ranks are 2–10.What is the probability of spades?5.A–KDraw one card from a well-shuffledstandard 52-card deck with no jokers.Face cards are J, Q, and K; an ace isseparate; numeric ranks are 2–10.What is the probability of 4?6.A–KDraw one card from a well-shuffledstandard 52-card deck with no jokers.Face cards are J, Q, and K; an ace isseparate; numeric ranks are 2–10.What is the probability of Q?7.A–KDraw a card, replace it, shuffle, and drawagain from a standard 52-card deck withno jokers. Face cards are J, Q, and K; anace is separate; numeric ranks are2–10.What is the probability of draw 1: ace and draw 2: 2?8.A–KDraw one card from a well-shuffledstandard 52-card deck with no jokers.Face cards are J, Q, and K; an ace isseparate; numeric ranks are 2–10.What is the probability of clubs and numeric rank from 2through 6?9.A–KDraw one card from a well-shuffledstandard 52-card deck with no jokers.Face cards are J, Q, and K; an ace isseparate; numeric ranks are 2–10.What is the probability of 3?10.A–KDraw a card, replace it, shuffle, and drawagain from a standard 52-card deck withno jokers. Face cards are J, Q, and K; anace is separate; numeric ranks are2–10.What is the probability of draw 1: 4 and draw 2: 5?math-sheet.comPage 1 / 1

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