JEE Mains · Maths · STD 12 - 13. probability
Let \(N\) denotes the sum of the numbers obtained when two dice are rolled. If the probability that \(2^{ N } < N !\) is \(\frac{m}{n}\), where \(m\) and \(n\) are coprime, then \(4 m -3 n\) is equal to \(......\).
- A \(8\)
- B \(16\)
- C \(10\)
- D \(12\)
Answer & Solution
Correct Answer
(A) \(8\)
Step-by-step Solution
Detailed explanation
\(N =\) Sum of the numbers when two dice are rolled such that \(2^{ N } < N\) ! \(\Rightarrow 4 \leq N \leq 12\) Probability that \(2^N \geq N\) ! \(\text { Now } P(N=2)+P(N=3)=\frac{1}{36}+\frac{2}{36}=\frac{3}{36}=\frac{1}{12}\)…
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