14.3 Classic Probability Scenarios: Coins, Dice, and Cards

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Key Formulas

Solved Examples

Step 1

  1. Total Outcomes: The deck has 52 cards. Total outcomes = 52.

Step 2

  1. (i) An Ace: There are 4 aces in the deck (one of each suit). Favorable outcomes = 4. P(Ace)=452=113P(\text{Ace}) = \frac{4}{52} = \frac{1}{13}

Step 3

  1. (ii) Not an Ace: This is the complementary event. P(Not Ace)=1−P(Ace)P(\text{Not Ace}) = 1 - P(\text{Ace}). P(Not Ace)=1−113=1213P(\text{Not Ace}) = 1 - \frac{1}{13} = \frac{12}{13}

Step 4

  1. Alternative Logic for (ii): Total cards that are not aces = 52−4=4852 - 4 = 48. Probability = 48/52=12/1348/52 = 12/13.
Final Answer

(i) 1/13, (ii) 12/13

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