Q49 / 90 · JEE Main 2024 (09 Apr Shift 2) · Mathematics

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text {th }}$ roll than the number obtained in the $(i-1)^{\text {th }}$ roll, $i=2,3$, is equal to

  • A
    $3 / 54$
  • B
    $2 / 54$
  • C
    $1 / 54$
  • Correct answer
    D
    $5 / 54$

Solution

Favourable cases $={ }^6 \mathrm{C}_3$ Total out comes $=6^3$ Probability of getting greater number than previous $\text {one }=\frac{{ }^6 \mathrm{C}_3}{\mathrm{r}^3}=\frac{20}{216}=\frac{5}{54}$

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

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