Question

In a large population 70% of the people speak English only, 20% of the people speak Spanish only, and 10% speak both English and Spanish . If we randomly sample two people from this population, what is the probability they will be able to speak the same language?

Answer 1

73% chance that they will be able to speak the same language

Explanation:

The probability that both people speak english will be 0.8*0.8 since we must account for bilingual people.

The probability that the both speak spanish is 0.3+0.3.

To have the total probability that both speak the same language we simply sum both propabilities.

0.8²+0.3²=0.73