A die is symmetrical but unusual: two of its faces have two points each, while the other four have one point each. Sergey rolled the die several times, and as a result, the sum of all the points that came up was 3. Find the probability that at some roll, a face with 2 points came up.

#
When rolling once, the probability of rolling a two is $p=1 / 3$, and the probability of rolling a one is $q=1-p=2 / 3$.

A total of 3 points could result from the following sequences:

$1,1,1$ - the probability of this is $q^{3}$.

2,1 or 1,2 - the probability of this is $2 p q$.

Therefore, the probability of one of the outcomes 1, 2 or 2,1 given that a total of 3 points was rolled is

$$
\frac{2 p q}{2 p q+q^{3}}=\frac{2 p}{2 p+q^{2}}=\frac{\frac{2}{3}}{\frac{2}{3}+\frac{4}{9}}=0.6
$$

## Answer

## $0.6$.