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What is the probability of having at least one ‘six’ from 3 throws of a perfect die?
- a)5/6
- b)(5/6)3
- c)1– (1/6)3
- d)1 – (5/6)3
Correct answer is option 'A'. Can you explain this answer?
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What is the probability of having at least one ‘six’ from ...
Solution:
The probability of getting a six on a single throw of a perfect die is 1/6.
To find the probability of having at least one six from 3 throws of a perfect die, we can use the complementary probability approach.
Complementary Probability Approach:
The complementary probability of an event A is the probability of the event not occurring (i.e., 1 minus the probability of A).
Let B be the event of not getting a six in a single throw of a perfect die. Then, the probability of B is:
P(B) = 1 - 1/6 = 5/6
Now, let C be the event of not getting a six in any of the 3 throws of a perfect die. Then, the probability of C is:
P(C) = P(B) × P(B) × P(B) (since the throws are independent)
P(C) = (5/6) × (5/6) × (5/6) = (5/6)3
Finally, the probability of having at least one six from 3 throws of a perfect die is:
P(at least one six) = 1 - P(C) (using the complementary probability)
P(at least one six) = 1 - (5/6)3 ≈ 0.4213
Therefore, the correct answer is option 'A' (5/6).
The probability of getting a six on a single throw of a perfect die is 1/6.
To find the probability of having at least one six from 3 throws of a perfect die, we can use the complementary probability approach.
Complementary Probability Approach:
The complementary probability of an event A is the probability of the event not occurring (i.e., 1 minus the probability of A).
Let B be the event of not getting a six in a single throw of a perfect die. Then, the probability of B is:
P(B) = 1 - 1/6 = 5/6
Now, let C be the event of not getting a six in any of the 3 throws of a perfect die. Then, the probability of C is:
P(C) = P(B) × P(B) × P(B) (since the throws are independent)
P(C) = (5/6) × (5/6) × (5/6) = (5/6)3
Finally, the probability of having at least one six from 3 throws of a perfect die is:
P(at least one six) = 1 - P(C) (using the complementary probability)
P(at least one six) = 1 - (5/6)3 ≈ 0.4213
Therefore, the correct answer is option 'A' (5/6).
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Community Answer
What is the probability of having at least one ‘six’ from ...
Correct answer is'd' .
Use formula P(A) = 1 - P(A')
Use formula P(A) = 1 - P(A')
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What is the probability of having at least one ‘six’ from 3 throws of a perfect die?a)5/6b)(5/6)3c)1– (1/6)3d)1 – (5/6)3Correct answer is option 'A'. Can you explain this answer?
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