Q75 / 160 · AP EAMCET 2022 (08 Jul Shift 2) · Mathematics

Three unbiased coins are tossed. Then, the probability of getting at most two heads is

  • A
    $3 / 4$
  • B
    $1 / 4$
  • C
    $3 / 8$
  • Correct answer
    D
    $7 / 8$

Solution

3 unbiased coins are tossed. Sample space, $S=\{$ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT $\}$ $n(S)=8$ Let $E$ be the event of getting at most two heads. $\Rightarrow E^{\prime}=\{\mathrm{HHH}\}$ $P(E)=1-P\left(E^{\prime}\right)=1-\frac{n\left(E^{\prime}\right)}{n(S)}=1-\frac{1}{8}=\frac{7}{8}$

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

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