Q257 / 270 · NDA 2018 (Phase 2) · Mathematics

8 coins are tossed simultaneously. The probability of getting at least 6 heads is

  • A
    $\frac{7}{64}$
  • B
    $\frac{57}{64}$
  • Correct answer
    C
    $\frac{37}{256}$
  • D
    $\frac{229}{256}$

Solution

In tossing of coin getting $r$ head out of $n$ tossing $={ }^n C_r \cdot\left(\frac{1}{2}\right)^n$ Required probability $\begin{aligned} & =\left({ }^8 \mathrm{C}_6+{ }^8 \mathrm{C}_7+{ }^8 \mathrm{C}_8\right)\left(\frac{1}{2}\right)^8 \\ & =(28+8+1) \times \frac{1}{256}=\frac{37}{256} \end{aligned}$

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

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