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What is the probability of having atleast one 6 from three throws of a perfect die?
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What is the probability of having atleast one 6 from three throws of a...
Understanding the Problem
To find the probability of rolling at least one 6 in three throws of a perfect die, we can use the complementary probability method.
Complementary Probability
1. Calculate the probability of NOT rolling a 6:
- The probability of rolling a number other than 6 on a single throw is 5/6.
2. Calculate the probability of NOT rolling a 6 in three throws:
- Since the throws are independent, multiply the probabilities:
- (5/6) x (5/6) x (5/6) = (5/6)^3
3. Calculate (5/6)^3:
- (5/6)^3 = 125/216
Calculating the Required Probability
1. Find the probability of rolling at least one 6:
- Use the complement rule:
- P(at least one 6) = 1 - P(no 6s)
- P(at least one 6) = 1 - (5/6)^3
- P(at least one 6) = 1 - 125/216
2. Final Calculation:
- P(at least one 6) = 216/216 - 125/216
- P(at least one 6) = 91/216
Conclusion
The probability of rolling at least one 6 in three throws of a perfect die is 91/216, which approximates to about 0.4213, or 42.13%.
This means there is a 42.13% chance of getting at least one 6 when throwing a die three times.
To find the probability of rolling at least one 6 in three throws of a perfect die, we can use the complementary probability method.
Complementary Probability
1. Calculate the probability of NOT rolling a 6:
- The probability of rolling a number other than 6 on a single throw is 5/6.
2. Calculate the probability of NOT rolling a 6 in three throws:
- Since the throws are independent, multiply the probabilities:
- (5/6) x (5/6) x (5/6) = (5/6)^3
3. Calculate (5/6)^3:
- (5/6)^3 = 125/216
Calculating the Required Probability
1. Find the probability of rolling at least one 6:
- Use the complement rule:
- P(at least one 6) = 1 - P(no 6s)
- P(at least one 6) = 1 - (5/6)^3
- P(at least one 6) = 1 - 125/216
2. Final Calculation:
- P(at least one 6) = 216/216 - 125/216
- P(at least one 6) = 91/216
Conclusion
The probability of rolling at least one 6 in three throws of a perfect die is 91/216, which approximates to about 0.4213, or 42.13%.
This means there is a 42.13% chance of getting at least one 6 when throwing a die three times.
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What is the probability of having atleast one 6 from three throws of a perfect die? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about What is the probability of having atleast one 6 from three throws of a perfect die? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the probability of having atleast one 6 from three throws of a perfect die?.
What is the probability of having atleast one 6 from three throws of a perfect die? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about What is the probability of having atleast one 6 from three throws of a perfect die? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the probability of having atleast one 6 from three throws of a perfect die?.
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