The number of students taking German or Spanish is 6 + 5 = 11. Of that group of 11, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 11 - 2 = 9 who are taking at least one language. 19 - 9 = 10 students who are not taking either language.

The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 5 factors [1, 2, 4, 8, 16] making 16 the greatest factor 32 and 80 have in common.

To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{40}{44} \) = \( \frac{\frac{40}{4}}{\frac{44}{4}} \) = \( \frac{10}{11} \)

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (3 + 4) ÷ 2 x 3 - 4²
P: 4 + (7) ÷ 2 x 3 - 4²
E: 4 + 7 ÷ 2 x 3 - 16
MD: 4 + \( \frac{7}{2} \) x 3 - 16
MD: 4 + \( \frac{21}{2} \) - 16
AS: \( \frac{8}{2} \) + \( \frac{21}{2} \) - 16
AS: \( \frac{29}{2} \) - 16
AS: \( \frac{29 - 32}{2} \)
\( \frac{-3}{2} \)
-1\(\frac{1}{2}\)

You have 6 out of the total of 150 raffle tickets sold so you have a (\( \frac{6}{150} \)) x 100 = \( \frac{6 \times 100}{150} \) = \( \frac{600}{150} \) = 4% chance to win the raffle.