Math Problem Statement
Solution
This problem involves calculating the probability of getting at least one "6" when a fair die is thrown four times. Let me solve it step by step:
Step 1: Probability of NOT getting a "6" in a single roll
For a fair die, the probability of getting any specific number (like "6") is . Therefore, the probability of NOT getting a "6" is:
Step 2: Probability of NOT getting a "6" in all four rolls
If the die is rolled four times, the events are independent. Thus, the probability of not getting a "6" in all four rolls is:
Let us compute this value:
Step 3: Probability of getting at least one "6"
The complement of "not getting a 6 in all rolls" is "getting at least one 6". Using the complement rule:
Substitute the value:
Final Answer:
The probability that Mai gets at least one "6" in four rolls of the die is:
Would you like further clarification or a deeper breakdown?
Here are 5 related questions for practice:
- What is the probability of getting exactly one "6" in four rolls of a fair die?
- What is the probability of getting no "6"s when the die is rolled six times?
- If a die is rolled three times, what is the probability of getting at least one even number?
- How does the probability of getting at least one "6" change if the die is rolled five times instead of four?
- What is the probability of getting at least two "6"s in four rolls of a fair die?
Tip: Always look for ways to simplify problems by using complementary probabilities, as it often reduces calculations.
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Math Problem Analysis
Mathematical Concepts
Probability
Independent Events
Complementary Probability
Formulas
P(Not 6 in one roll) = 1 - P(6 in one roll)
P(Not 6 in all rolls) = (P(Not 6 in one roll))^n
P(At least one 6) = 1 - P(Not 6 in all rolls)
Theorems
Complement Rule in Probability
Suitable Grade Level
Grades 9-12
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