26. What is the probability of getting a sum of 9 from simultaneously throwing two dice?
(1) 1/6       (2) 1/8
(3) 1/9       (4) 1/12

Step‑by‑step solution

1. Total possible outcomes

   • Each die has 6 faces, so for two dice:

     $$6\times 6=36\text{ outcomes}$$

2. Favourable outcomes for sum = 9

   • List all ordered pairs $(x,y)$ such that $x+y=9$:

     • (3, 6)

     • (4, 5)

     • (5, 4)

     • (6, 3)

   • Number of favourable outcomes = 4.​

3. Probability

   P(sum =9)=favourable outcomestotal outcomes=436=19P(sum =9)=total outcomesfavourable outcomes=364=91

So the correct option is (3) 1/9.

Why the other options are incorrect

• 1/6 – would correspond to 6 favourable outcomes (which would be sums with six pairs), more than actually exist for total 9.

• 1/8 – implies 4.5 favourable outcomes (impossible) and does not match the actual counting.

• 1/12 – corresponds to only 3 favourable outcomes; but there are 4 ordered pairs giving sum 9, not 3.

Thus, the probability of getting a sum of 9 from two dice is 1/9.