A tourist who speaks English but no other language visits a region of Germany. If 35% of the residents speak English, 15% speak German, and 3% speak both English and German, wha…

Question

asked Apr 25, 2021 77.8k views

1 Answer

Benjin · Answer 1 · 2021-04-30T19:33:31+0000

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

Explanation:

We use the conditional probability formula to solve this question. It is

$P(B|A) = (P(A \cap B))/(P(A))$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ 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
$P(A \cap B) = 0.03$

15% speak German

This means that
P(A) = 0.15

So

P(B|A) = (0.03)/(0.15) = 0.2

20% robability that the tourist will be able to talk with a randomly encountered resident of the region, given that the resident speaks German