Answer:
[tex]0.25[/tex].
Step-by-step explanation:
Using information from the table:
- [tex]20[/tex] out of the [tex]100[/tex] individuals are vegan. The probability that a person is vegan would be [tex]P(\text{Vegan}) = (20 / 100)[/tex].
- [tex]5[/tex] out of the [tex]100[/tex] individuals are vegan and allergic to nuts. The probability that a person is vegan and allergic to nuts would be [tex]P(\text{Allergic to Nuts $\cap$ Vegan}) = (5 / 100)[/tex].
Let [tex]P(\text{Allergic to nuts} | \text{Vegan})[/tex] denote the probability that the person is allergic to nuts given that this person is vegan.
By the property of conditional probabilities:
[tex]\begin{aligned}P(\text{Allergic to nuts} | \text{Vegan}) &= \frac{P(\text{Allergic to nuts $\cap$ Vegan)})}{P(\text{Vegan})} \\ &= \frac{(5 / 100)}{(20 / 100)} \\ &= 0.25\end{aligned}[/tex].
