Math Problem Statement
Solution
To solve the problem, we must determine which outcomes satisfy each event and calculate the probability.
Events and Steps:
-
Outcomes: The possible outcomes are:
- EOO, OEO, EOE, EEE, EEE, OOE, OOO, EEO
(8 outcomes total, where each outcome represents even/odd results across 3 rolls.)
- EOO, OEO, EOE, EEE, EEE, OOE, OOO, EEO
-
Probability of Each Outcome: Since all outcomes are equally likely, the probability of each outcome is:
Event A: An even number on the last roll or the second roll (or both).
- Focus on outcomes where the second roll or last roll (or both) is even.
- Outcomes that satisfy Event A:
- EOO, OEO, EOE, EEE, EEO
- Total outcomes = 5
- Probability:
Event B: More even numbers than odd numbers.
- An outcome has more even numbers if at least 2 positions are even (e.g., EEE, EEO, etc.).
- Outcomes that satisfy Event B:
- EOE, EEE, EEO
- Total outcomes = 3
- Probability:
Event C: Two or more even numbers.
- Focus on outcomes with at least 2 even numbers.
- Outcomes that satisfy Event C:
- EOE, EEE, EEO
- Total outcomes = 3
- Probability:
Final Table:
Event | Outcomes Satisfied | Probability |
---|---|---|
Event A | EOO, OEO, EOE, EEE, EEO | |
Event B | EOE, EEE, EEO | |
Event C | EOE, EEE, EEO |
Would you like a detailed explanation for any specific event or further clarifications?
5 Related Questions:
- How do you calculate probabilities for equally likely outcomes?
- What are the differences between "at least two" and "more than two" conditions?
- How would probabilities change if we added a fourth roll?
- Can you explain complementary events and how they relate to these probabilities?
- How do we use probability in real-world situations like dice games?
Tip: Always verify the outcomes carefully to ensure none are missed when counting for specific events.
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Math Problem Analysis
Mathematical Concepts
Probability
Equally likely outcomes
Events and outcomes
Formulas
P(each outcome) = 1/8
Theorems
Basic probability theorem
Equally likely outcomes principle
Suitable Grade Level
Grades 6-8
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