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?

Question

Mathematics

Maia Norton

20 March, 19:24

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?

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Answers (1)

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Nancy Huffman · Answer 1

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

Step-by-step 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