<s>[INST] Probability about oranges There are $15$ oranges in each bag.
Each orange has a probability of $10$% to be bad-looking.
Supermarkets only sell the bags that have $12$ or more good-looking oranges.  

What percentage of all the bags will be sold?

 [/INST] Compute: 
$$ 
\ \ \ \ 
{15 \choose 3} \cdot Pr(3 \ \text{bad-look oranges}) 
\cdot Pr(12 \ \text{good-look oranges}) 
\\ + 
{15 \choose 2} \cdot Pr(2 \ \text{bad-look oranges}) 
\cdot Pr(13 \ \text{good-look oranges}) \\ + 
{15 \choose 1} \cdot Pr(1 \ \text{bad-look oranges}) 
\cdot Pr(14 \ \text{good-look oranges}) \\ + 
Pr(15 \ \text{good-look oranges}) \\ = 
{15 \choose 3} \cdot (\dfrac{1}{10})^3 \cdot (\dfrac{9}{10})^{12} + 
{15 \choose 2} \cdot (\dfrac{1}{10})^2 \cdot (\dfrac{9}{10})^{13} + 
{15 \choose 1} \cdot (\dfrac{1}{10})   \cdot (\dfrac{9}{10})^{14} + 
(\dfrac{9}{10})^{15} 
$$
</s>