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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).
If you randomly pick your kind of pasta and flavor, what is the probability that you'll end up with bow ties, cheese sauce, or both?

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 bow ties, cheese sauce, or both?

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Find probabilities using combinations and permutations

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 bow ties, cheese sauce, or both?

Calculate total combinations: There are $5$ kinds of pasta and $4$ flavors, so there are $5 \times 4 = 20$ total combinations.
Calculate bow ties combinations: For bow ties with any flavor, there are $4$ combinations since there are $4$ flavors.
Calculate cheese sauce combinations: For cheese sauce with any pasta, there are $5$ combinations since there are $5$ kinds of pasta.
Adjust for duplicate count: We counted bow ties with cheese sauce twice, so we subtract $1$ from the total.
Calculate total favorable combinations: Adding the combinations for bow ties and cheese sauce, we get $4 + 5 - 1 = 8$ combinations.
Calculate probability: The probability is the number of favorable outcomes over the total number of outcomes, so it's $\frac{8}{20}.$
Simplify fraction: Simplify the fraction $\frac{8}{20}$ to get $\frac{2}{5}$ .
Convert to decimal: Convert the fraction to a decimal to get $0.4$ .

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