Using probability of independent events, it is found that there is a [tex]\frac{2}{9}[/tex] probability that Janelle will add a scarf and boots (tall or short) to her outfit.
Independent Events:
- If two events, A and B, are independent, the probability of both happening is the multiplication of the probability of each happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this problem, the events are:
- Event A: Scarf, which has probability [tex]P(A) = \frac{1}{3}[/tex].
- Event B: Boots, which has probability [tex]P(B) = \frac{1}{2} + \frac{1}{6} = \frac{4}{6} = \frac{2}{3}[/tex]
Hence:
[tex]P(A \cap B) = P(A)P(B) = \frac{1}{3} \times \frac{2}{3} = \frac{2}{9}[/tex]
[tex]\frac{2}{9}[/tex] probability that Janelle will add a scarf and boots (tall or short) to her outfit.
To learn more about probability of independent events, you can take a look at https://brainly.com/question/25715148