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?

Compute:

$$ \ \ \ \ {15 \choose 3} \cdot Pr(3 \ \text{bad-look oranges}) \cdot Pr(12 \ \text{good-look oranges}) \\\ + {15 \choose 2} \cdot Pr(2 \ \text{bad-look oranges}) \cdot Pr(13 \ \text{good-look oranges}) \\\ + {15 \choose 1} \cdot Pr(1 \ \text{bad-look oranges}) \cdot Pr(14 \ \text{good-look oranges}) \\\ + Pr(15 \ \text{good-look oranges}) \\\ = {15 \choose 3} \cdot (\dfrac{1}{10})^3 \cdot (\dfrac{9}{10})^{12} + {15 \choose 2} \cdot (\dfrac{1}{10})^2 \cdot (\dfrac{9}{10})^{13} + {15 \choose 1} \cdot (\dfrac{1}{10}) \cdot (\dfrac{9}{10})^{14} + (\dfrac{9}{10})^{15} $$