1. **Problem:** Describe an outcome that is certain when selecting one card from a standard deck of 52 cards. 2. **Formula and rules:** The probability of a certain event is always 1 because it will definitely happen. 3. **Work:** Since the deck has 52 cards, selecting any card is certain. 4. **Explanation:** The outcome "selecting a card from the deck" is certain because the deck only contains playing cards. --- 1. **Problem:** Describe a different outcome equally likely to selecting a diamond card. 2. **Formula and rules:** Probability of selecting a card from a suit = $\frac{\text{number of cards in suit}}{\text{total cards}}$. 3. **Work:** Diamonds have 13 cards, hearts also have 13 cards. 4. **Explanation:** Selecting a heart card is equally likely as selecting a diamond card because both suits have 13 cards out of 52. --- 1. **Problem:** For which outcome is the probability $\frac{1}{13}$? Options: Selecting a King, Selecting a heart, Selecting the King of hearts. 2. **Formula and rules:** Probability of a specific card = $\frac{1}{52}$, probability of a rank (like King) = $\frac{4}{52} = \frac{1}{13}$. 3. **Work:** - Selecting a King: 4 Kings in deck, probability $= \frac{4}{52} = \frac{1}{13}$. - Selecting a heart: 13 hearts, probability $= \frac{13}{52} = \frac{1}{4}$. - Selecting the King of hearts: 1 card, probability $= \frac{1}{52}$. 4. **Explanation:** The probability $\frac{1}{13}$ corresponds to selecting a King. --- 1. **Problem:** Effects of missing 9 of clubs on probabilities. 2. **a. Less likely event:** Selecting the 9 of clubs. - Since the 9 of clubs is missing, probability is 0, less than expected $\frac{1}{52}$. 3. **b. More likely event:** Selecting a heart. - Total cards now 51, hearts still 13. - Probability $= \frac{13}{51} > \frac{13}{52}$, so more likely. 4. **c. Equally likely event:** Selecting the King of hearts. - Only one King of hearts, probability $= \frac{1}{51}$ vs $\frac{1}{52}$, very close, effectively equally likely. --- **Final answers:** 1. Certain outcome: Selecting any card from the deck. 2. Equally likely outcome to diamonds: Selecting hearts. 3. Probability $\frac{1}{13}$ outcome: Selecting a King. 4. a) Less likely: Selecting 9 of clubs. b) More likely: Selecting a heart. c) Equally likely: Selecting King of hearts.