Q266 / 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 $p+q$ ?

  • Correct answer
    A
    $\frac{57}{32}$
  • B
    $\frac{53}{32}$
  • C
    $\frac{51}{32}$
  • D
    1

Solution

$\begin{aligned} p+q & =2-2\left(\frac{1}{2}\right)^n-\frac{n}{2^n} \\ & =2-2 \times \frac{1}{2^5}-\frac{5}{2^5}=\frac{57}{32}\end{aligned}$

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

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