Question

Ana is having dinner with her parents at Bellini in Weston that serves 5 kinds of pasta (penne, rigatoni, angel hair, cannelloni, and tortellini) in 4 different flavors (four cheese, pesto, pink sauce, and bolognese).
If Ana randomly picks one kind of pasta and flavor, what is the probability that Ana ends up with rigatoni, pink sauce, or both?

Enter your answer as a simplified fraction. Use / to write your fraction.

The probability is [a]
plz, help!!

Answer 1

Answer: $\dfrac{2}{5}$.

Step-by-step explanation:

Given : Total kinds of pasta = 5

Total kinds of flavors = 4

The probability of selecting rigatoni = P(rigatoni) = $\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}=\dfrac{1}{5}$

The probability of selecting pink sauce = P(pink sauce) = $\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}=\dfrac{1}{4}$

Since both kinds and flavour are basically independent factor to get choose.

So, P(rigatoni and pink sauce)= P(rigatoni) x P(pink sauce)

$=\dfrac{1}{5}\times\dfrac{1}{4}=\dfrac{1}{20}$

Now , the  probability that Ana ends up with rigatoni, pink sauce, or both would be :

P(rigatoni or pink sauce) = P(rigatoni) + P(pink sauce) - P(rigatoni and pink sauce)

$=\dfrac{1}{5}+\dfrac{1}{4}-\dfrac{1}{20}\\\\=\dfrac{4+5-1}{20}=\dfrac{2}{5}$

Hence, the required probability is $\dfrac{2}{5}$.