Respuesta :
Answer:
20% robability that the tourist will be able to talk with a randomly encountered resident of the region, given that the resident speaks German
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this problem, we have that:
Event A: Speaking German
Event B: Speaking English
3% speak both English and German
This means that [tex]P(A \cap B) = 0.03[/tex]
15% speak German
This means that [tex]P(A) = 0.15[/tex]
So
[tex]P(B|A) = \frac{0.03}{0.15} = 0.2[/tex]
20% robability that the tourist will be able to talk with a randomly encountered resident of the region, given that the resident speaks German
