You have 8 out of the total of 200 raffle tickets sold so you have a (\( \frac{8}{200} \)) x 100 = \( \frac{8 \times 100}{200} \) = \( \frac{800}{200} \) = 4% chance to win the raffle.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{3 x 5}{2 x 5} \) + \( \frac{2 x 1}{10 x 1} \)

\( \frac{15}{10} \) + \( \frac{2}{10} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{15 + 2}{10} \) = \( \frac{17}{10} \) = 1\(\frac{7}{10}\)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{8} \) x \( \frac{1}{6} \) = \( \frac{2 x 1}{8 x 6} \) = \( \frac{2}{48} \) = \(\frac{1}{24}\)

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{7}{100} \) x 9 = \( \frac{7 \times 9}{100} \) = \( \frac{63}{100} \) = 0.63 errors per hour

So, in an average hour, the machine will produce 9 - 0.63 = 8.37 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 8.37 = 133.9 error free parts were produced yesterday.