JEE Mains · Maths · STD 11 - 14. probability
Let a die be rolled \(n\) times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is \(\frac{ k }{2^{15}}\), then \(k\) is equal to:
- A \(30\)
- B \(90\)
- C \(15\)
- D \(60\)
Answer & Solution
Correct Answer
(D) \(60\)
Step-by-step Solution
Detailed explanation
\(P\) (odd number 7 times) \(= P\) (odd number 9 times) \({ }^{ n } C _7\left(\frac{1}{2}\right)^7\left(\frac{1}{2}\right)^{ n -7}={ }^{ n } C _9\left(\frac{1}{2}\right)^9\left(\frac{1}{2}\right)^{ n -9}\) \({ }^{ n } C _7={ }^{ n } C _9\) \(\Rightarrow n =16\) Required…
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