Probability E-Note for Senior Secondary School | Edwin Ogie Library 3

 

Understanding a Standard Deck of Cards with Probability Examples

A standard deck of playing cards contains 52 cards, divided into four suits:

1. Hearts (♥) – 13 cards
2. Diamonds (♦) – 13 cards
3. Clubs (♣) – 13 cards
4. Spades (♠) – 13 cards

Each suit has:

• 9 Numbered Cards: 2, 3, 4, 5, 6, 7, 8, 9, and 10
• 3 Face Cards: Jack (J), Queen (Q), and King (K)
• 1 Ace (A)

Since there are four suits, the deck contains:

• 4 Aces: A♠, A♥, A♦, A♣
• 12 Face Cards: J♠, J♥, J♦, J♣, Q♠, Q♥, Q♦, Q♣, K♠, K♥, K♦, K♣
• 36 Numbered Cards

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Probability Examples with a Standard Deck of Cards

Example 1: Probability of Drawing an Ace

$$\text{Probability} = \frac{\text{Number of Aces}}{\text{Total Cards}}$$ $$\frac{4}{52} = \frac{1}{13} \approx 7.69\%$$

Example 2: Probability of Drawing a Face Card (J, Q, K)

There are 12 face cards in the deck.

$$\text{Probability} = \frac{\text{Number of Face Cards}}{\text{Total Cards}}$$ $$\frac{12}{52} = \frac{3}{13} \approx 23.08\%$$

Example 3: Probability of Drawing a Red Card (Hearts or Diamonds)

There are 26 red cards (13 Hearts + 13 Diamonds).

$$\text{Probability} = \frac{26}{52} = \frac{1}{2} = 50\%$$

Example 4: Probability of Drawing a Black Card (Spades or Clubs)

There are 26 black cards (13 Spades + 13 Clubs).

$$\text{Probability} = \frac{26}{52} = \frac{1}{2} = 50\%$$

Example 5: Probability of Drawing a King of Hearts (K♥)

Since there is only one King of Hearts in the deck:

$$\text{Probability} = \frac{1}{52} \approx 1.92\%$$

Example 6: Probability of Drawing a Numbered Card (2 to 10)

There are 9 numbered cards in each suit, so a total of:

$$9 \times 4 = 36 \text{ (Total Numbered Cards)}$$ $$\text{Probability} = \frac{36}{52} = \frac{9}{13} \approx 69.23\%$$

Example 7: Probability of Drawing a Jack or a Queen

There are 4 Jacks and 4 Queens, making a total of 8 cards.

$$\text{Probability} = \frac{8}{52} = \frac{2}{13} \approx 15.38\%$$

Example 8: Probability of Drawing a Club (♣)

There are 13 Clubs in the deck.

$$\text{Probability} = \frac{13}{52} = \frac{1}{4} = 25\%$$

Example 9: Probability of Drawing an Even Numbered Card (2, 4, 6, 8, 10)

Each suit has five even-numbered cards (2, 4, 6, 8, 10).
Since there are four suits:

$$5 \times 4 = 20 \text{ (Total Even-Numbered Cards)}$$ $$\text{Probability} = \frac{20}{52} = \frac{5}{13} \approx 38.46\%$$

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These examples help illustrate how probabilities are calculated using a standard deck of 52 cards.