Q79 / 160 · TS EAMCET 2023 (14 May Shift 2) · Mathematics

There are 10 coins in a box out of which 8 are normal and the remaining are with heads on both sides. A coin is chosen at random from the box and tossed 6 times. If it shows heads each time, then the probability that the selected coin has head on both sides is

  • Correct answer
    A
    $\frac{16}{17}$
  • B
    $\frac{32}{41}$
  • C
    $\frac{8}{9}$
  • D
    $\frac{12}{13}$

Solution

$P($ both side head $)=\frac{2}{10}$ $P($ Fair coin $)=\frac{8}{10}$ $\begin{aligned} & P\left(\frac{\text { Head }}{\text { Fair }}\right)=\left(\frac{1}{2}\right)^6 \\ & P\left(\frac{\text { Head }}{\text { Unfair }}\right)=1\end{aligned}$ Probability $=\frac{\frac{2}{10} \times 1}{\frac{2}{10} \times 1+\left(\frac{1}{2}\right)^6 \times \frac{8}{10}}=\frac{16}{17}$

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

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