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11 Oct 2021, 09:55
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A fair six-sided dice was rolled \(n\) times. What is the value of \(n\)?
(1) The number of different possible sequences of \(n\)-digit numbers when a dice is rolled \(n\) times is 7776.
(2) If the dice has been rolled 3 times fewer, the probability of getting a 6 on every roll would have been \(\frac{1}{36}\).
(1) The number of different possible sequences of \(n\)-digit numbers when a dice is rolled \(n\) times is 7776.
(2) If the dice has been rolled 3 times fewer, the probability of getting a 6 on every roll would have been \(\frac{1}{36}\).
11 Oct 2021, 09:56
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Official Solution:
A fair six-sided dice was rolled \(n\) times. What is the value of \(n\)?
(1) The number of different possible sequences of \(n\)-digit numbers when a dice is rolled \(n\) times is 7776.
When rolling a die \(n\) times, each roll can result in a number from 1 through 6 (6 values), thus total of \(6^n\) different sequences of numbers when rolling \(n\) times.
This means that \(6^n = 7776\). We can get the value of \(n\) (\(n=5\)). Sufficient.
(2) If the dice has been rolled 3 times fewer, the probability of getting a 6 on every roll would have been \(\frac{1}{36}\).
This means that \((\frac{1}{6})^{(n - 3)} = \frac{1}{36}\);
\((\frac{1}{6})^{(n - 3)} = (\frac{1}{6})^{2}\);
\(n-3=2\);
\(n=5\). Sufficient.
Answer: D
A fair six-sided dice was rolled \(n\) times. What is the value of \(n\)?
(1) The number of different possible sequences of \(n\)-digit numbers when a dice is rolled \(n\) times is 7776.
When rolling a die \(n\) times, each roll can result in a number from 1 through 6 (6 values), thus total of \(6^n\) different sequences of numbers when rolling \(n\) times.
This means that \(6^n = 7776\). We can get the value of \(n\) (\(n=5\)). Sufficient.
(2) If the dice has been rolled 3 times fewer, the probability of getting a 6 on every roll would have been \(\frac{1}{36}\).
This means that \((\frac{1}{6})^{(n - 3)} = \frac{1}{36}\);
\((\frac{1}{6})^{(n - 3)} = (\frac{1}{6})^{2}\);
\(n-3=2\);
\(n=5\). Sufficient.
Answer: D
12 Feb 2025, 08:12
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I like the solution - it’s helpful.
