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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Probability

NDA 2024 · Mathematics · Probability

An unbiased coin is tossed n times. The probability of getting at...

An unbiased coin is tossed nn times. The probability of getting at least one tail is pp and the probability of at What is the value of nn ?

Options

  1. A4
  2. B5
  3. C6
  4. D7

Correct answer

B. 5

Step-by-step solution

p−q=532p-q=\frac{5}{32}⇒1−(12)n−[1−(12)n−n2n]=532⇒n2n=532⇒n2n=525\begin{aligned} \Rightarrow & 1-\left(\frac{1}{2}\right)^n-\left[1-\left(\frac{1}{2}\right)^n-\frac{n}{2^n}\right] & =\frac{5}{32} \\ \Rightarrow & \frac{n}{2^n} & =\frac{5}{32} \\ \Rightarrow & \frac{n}{2^n} & =\frac{5}{2^5} \end{aligned} Comparing both sides, we get, n=5n=5
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