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Home » Thus, the condition for \( f(x) \) to have exactly one real root is: - Get link 4share

Thus, the condition for \( f(x) \) to have exactly one real root is: - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A number greater than 4 corresponds to a 5 or 6. The probability of rolling a number greater than 4 on a single roll is:

📌 \frac{2}{6} = \frac{1}{3}

📌 The probability of rolling a number 4 or less is:

📌 \frac{4}{6} = \frac{2}{3}

📌 We want exactly two rolls to be greater than 4. The number of ways to choose which two of the three rolls are greater than 4 is:

📌 \binom{3}{2} = 3

📌 For each such choice, the probability is:

📌 \left(\frac{1}{3}\right)^2 \times \left(\frac{2}{3}\right)^1 = \frac{1}{9} \times \frac{2}{3} = \frac{2}{27}

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📝 Recent Posts

\(4\) → (4,0,0): All 4 in one archive
Number of ways: \(\binom{4}{4} = 1\), and only one way to assign indis...
\(3,1\) → (3,1,0): One archive has 3, another has 1
Number of ways: \(\binom{4}{3} = 4\) (choose 3 to go to the 3-element...
Since the two non-empty groups have different sizes, no symmetry — all...
\(2,2\) → (2,2,0): Two archives have 2 each, one empty
Number of ways: \(\frac{1}{2} \binom{4}{2} = \frac{1}{2} \cdot 6 = 3\)...
Alternatively: number of ways to partition 4 labeled items into two un...
\frac{1}{2} \binom{4}{2} = 3
\(2,1,1\) → (2,1,1): One archive has 2, two have 1

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