youre having dinner at a restaurant that serves 5 kinds of pasta (spaghetti, bow ties, fettuccine, ravioli…

youre 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 youll end up with bow ties, cheese sauce, or both?

youre 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 youll end up with bow ties, cheese sauce, or both?

Answer

Explanation:

Step1: Calculate total combinations

The total number of pasta - flavor combinations is the product of the number of pasta types and the number of flavors. So, $n = 5\times4=20$.

Step2: Calculate number of favorable cases

The number of cases with bow - ties is 4 (since there are 4 flavors for bow - ties). The number of cases with cheese sauce is 5 (since there are 5 types of pasta with cheese sauce). The number of cases with both bow - ties and cheese sauce is 1. Using the inclusion - exclusion principle, the number of favorable cases $m=4 + 5-1=8$.

Step3: Calculate probability

The probability $P$ is the number of favorable cases divided by the total number of cases. So, $P=\frac{m}{n}=\frac{8}{20}=\frac{2}{5}$.

Answer:

$\frac{2}{5}$