Three symmetrical dice are thrown. The probability of obtaining a sum of $5$ points is
- $\dfrac{1}{6}$
- $\dfrac{1}{36}$
- $\dfrac{1}{216}$
- $\dfrac{1}{54}$
Total outcomes for 3 dice is 6^3 = 216. Outcomes summing to 5 are (1,1,3), (1,3,1), (3,1,1), (1,2,2), (2,1,2), (2,2,1). There are 6 such outcomes. Probability = 6/216 = 1/36.
When three symmetrical dice are thrown, the total number of possible outcomes in the sample space is 6^3, which equals 216. To obtain a sum of 5 points, the specific combinations of numbers on the three dice must be permutations of (1, 1, 3) or (1, 2, 2). The combination (1, 1, 3) can be arranged in 3 ways, and the combination (1, 2, 2) can also be arranged in 3 ways, yielding a total of 6 favorable outcomes. Using the classical probability formula, the probability is 6 divided by 216, which simplifies to 1/36.