Q265 / 270 · NDA 2024 (Phase 1) · Mathematics

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

  • A
    4
  • Correct answer
    B
    5
  • C
    6
  • D
    7

Solution

$p-q=\frac{5}{32}$ $\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, $n=5$

Hence, the correct answer is option: 'B'.

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