Q115 / 170 · Manipal (MET) 2020 · Mathematics

A die is rolled three times. The probability of getting a larger number than the previous number is

  • A
    $\frac{5}{216}$
  • Correct answer
    B
    $\frac{5}{54}$
  • C
    $\frac{1}{6}$
  • D
    $\frac{5}{36}$

Solution

When a die is rolled three times. Then, cardinality of sample space $=6^3$ Now, according to question, the favourable outcomes $\begin{aligned}= & \{(1,2,3),(1,2,4),(1,2,5),(1,2,6), \\ & (1,3,4),(1,3,5),(1,3,6),(1,4,5), \\ & (1,4,6),(1,5,6),(2,3,4),(2,3,5), \\ & (2,3,6),(2,4,5),(2,4,6),(3,4,5), \\ & (3,4,6),(4,5,6),(2,5,6),(3,5,6)\}\end{aligned}$ $\therefore$ Required probability $=\frac{20}{6^3}=\frac{5}{54}$

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

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