Allied & ICAR Exam Bank • ALLIED_1011NAT • 2 Marks
Section 1: Engineering Mathematics
Probability and Statistics
Subtopic: Sampling theorems
Question Statement:
If a fair 6-sided die is rolled 3 times independently, the probability that the sum of the three rolls is at least 4 is:
Answer Key:
0.995
Step-by-Step Solution & Explanation
Total possible outcomes $= 6^3 = 216$. The minimum possible sum is $1+1+1=3$, which occurs in only 1 outcome $(1,1,1)$. All other $216 - 1 = 215$ outcomes yield a sum $\ge 4$. Probability $= \frac{215}{216} \approx 0.9954$.