Probability
Strictly Increasing Sequence — Dice Rolls
nta_pyq_2024_apr
Grade 12
Question:
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
Step-by-Step Solution
Key Concept: Need strictly increasing sequence of 3 outcomes from $\{1,2,3,4,5,6\}$. Favourable: choose any 3 distinct values and arrange in increasing order: $^6C_3=20$.
$P=^6C_3/6^3=20/216=5/54$.
Correct Answer: 4