Question

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, what is the probability that the tourist will be able to talk with a randomly encountered resident of the region, given that the resident speaks German

Answer 1

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