Two dice are thrown. The probability of getting a sum of less than $7$ points or a double is :
- $\frac{1}{6}$
- $\frac{1}{3}$
- $\frac{2}{3}$
- $\frac{1}{2}$
Total outcomes = 36. Sum < 7: (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), (5,1) = 15 outcomes. Doubles: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) = 6 outcomes. Union: 15 + 6 - 3 (overlaps: 1,1; 2,2; 3,3) = 18 outcomes. Probability = 18/36 = 1/2.
When two dice are thrown, the total number of possible outcomes is 36. The outcomes for getting a sum less than 7 are (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), and (5,1), yielding 15 combinations. Using the addition theorem of probability, the probability is the favorable outcomes divided by the total outcomes, which is 15/36. Simplifying this fraction gives 1/2.