You're having dinner at a restaurant that serves $5$ kinds of pasta (spaghetti, bow ties, fettuccine, ravioli, and macaroni) in $4$ different flavors (tomato sauce, cheese sauce, meat sauce, and olive oil). $\newline$ If you randomly pick your kind of pasta and flavor, what is the probability that you'll end up with something other than tomato spaghetti?

Full solution

Q. You're having dinner at a restaurant that serves

5

kinds of pasta (spaghetti, bow ties, fettuccine, ravioli, and macaroni) in

4

different flavors (tomato sauce, cheese sauce, meat sauce, and olive oil).

\newline

If you randomly pick your kind of pasta and flavor, what is the probability that you'll end up with something other than tomato spaghetti?

Calculate total combinations: Calculate the total number of pasta and sauce combinations. There are $5$ kinds of pasta and $4$ sauces, so $5 \times 4 = 20$ total combinations.
Find non-tomato spaghetti combos: Find the number of combinations that are NOT tomato spaghetti. Since there's only $1$ tomato spaghetti combo, there are $20 - 1 = 19$ other combos.
Calculate probability: Calculate the probability of not getting tomato spaghetti. The probability is the number of non-tomato spaghetti combos divided by the total number of combos, so $\frac{19}{20}$ .
Convert to percentage: Convert the probability to a percentage. Multiply the probability by $100$ to get the percentage, so $(\frac{19}{20}) \times 100 = 95\%$ .