Q77 / 160 · TS EAMCET 2019 (03 May Shift 1) · Mathematics

If five dice are thrown simultaneously, then the probability that atleast three of them show the same numbered face is

  • A
    $\frac{16}{6^4}$
  • B
    $\frac{452}{6^5}$
  • Correct answer
    C
    $\frac{276}{6^4}$
  • D
    $\frac{123}{6^5}$

Solution

Five dice are thrown simuItaneous $n=5, p=$ probability of show same numbered face $\therefore p=\frac{1}{6}, q=1-\frac{1}{6}=\frac{5}{6}$ $\therefore$ Required probability $=6(P(r \geq 3))=6[P(r=3)+P(r=4)+P(r=5)]$ $=6\left[{ }^5 C_3\left(\frac{1}{6}\right)^3\left(\frac{5}{6}\right)^2+{ }^5 C_4\left(\frac{1}{6}\right)^4 \frac{5}{6}+\left(\frac{1}{6}\right)^5\right]$ $=\frac{6}{6^5}(10 \times 25+25+1)=\frac{276}{6^4}$

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

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