What is the probability with two dice

a) when rolled once, to roll more than 9?

b) when rolled three times in a row, to roll less than 6 each time?

(For the example, see the article titled 》Elements of Probability Theory《 in this issue.)
When rolling two dice, the number of possible outcomes is $V_{6}^{i, 2}=6^{2}=36$.

a) Rolls with a value greater than 9: $6+6,6+5,5+6,6+4,4+6,5+5$, which means the number of favorable outcomes is 6, and thus the sought probability is

$$
v_{1}=\frac{6}{36}=\frac{1}{6}(\approx 0.167)
$$

b) There are 10 ways to roll less than 6: $1+1,1+2,2+1,1+3,3+1,2+2,1+4,4+1,2+3$, $3+2$. Since the number of favorable outcomes is 10, the probability of rolling less than 6 in one roll is: $\frac{10}{36}=\frac{5}{18}$. Since the 3 rolls are independent, according to the multiplication rule, the sought probability is

$$
v_{2}=\left(\frac{5}{18}\right)^{3}=\frac{125}{5832}(\approx 0.021)
$$

Beke Éva and Mária (Bp. XIII., Mechanical Engineering Technology II. class)