Purpose: Assess prerequisite skills from Chapters 1–3 before the probability unit: counting, basic probability, fractions/decimals, and use of conditional reasoning.
Prerequisite Knowledge
Question 1 [2 marks]
A jar has 5 red and 7 blue marbles. State, as fractions in lowest terms:
a) \( P(\text{red}) \) b) \( P(\text{not red}) \) c) \( P(\text{red}) + P(\text{blue}) \)
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Question 2 [3 marks]
A 5-card hand is drawn from a 52-card deck. Use combinations to find:
a) Number of possible 5-card hands
b) Number of hands containing all 4 Aces (and 1 other card)
c) Probability of (b)
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Question 3 [3 marks]
Convert each fraction to a decimal (4 places) and a percent:
a) \( \dfrac{3}{8} \) b) \( \dfrac{7}{36} \) c) \( \dfrac{1}{52} \)
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Question 4 [3 marks]
In a class, 60% study French, 30% study Spanish, and 20% study both. Use a Venn diagram or table to find:
a) \( P(\text{French only}) \)
b) \( P(\text{French OR Spanish}) \)
c) \( P(\text{neither}) \)
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Question 5 [3 marks]
A weighted average problem: A student scored 80% on Test 1 (worth 30%), 70% on Test 2 (worth 30%), and 90% on the Final (worth 40%). Compute the overall percentage. Explain how this is conceptually similar to expected value.
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Question 6 [3 marks]
Reflection: What do you find most challenging about probability so far — the language ("OR" vs "AND"), choosing the right counting method, or interpreting word problems? Be specific.