Question

consider the following venn diagram, depicting the data from surveying random individuals passing by on the street at a neighborhood in chicago about what second language (other than english) they could speak. data a) how many passersby could speak only russian as a second language? b) how many passersby could speak all three languages as the second language? c) how many passersby could speak both chinese and spanish as the second language, but not russian? d) how many passersby could speak chinese as the second language? e) how many passersby could speak either chinese or russian as the second language, or both chinese and russian, but no spanish at all? f) how many passersby could speak spanish as the second language?

Explanation:

Step1: Find only Russian speakers

In the Venn diagram, the number of people who speak only Russian is the value in the "SPEAKS RUSSIAN" circle that does not overlap with the other two circles. So it is \(30\).

Step2: Find all - three - language speakers

The number of people who speak all three languages is the value in the intersection of all three circles. So it is \(8\).

Step3: Find Chinese and Spanish but not Russian speakers

The number of people who speak Chinese and Spanish but not Russian is the value in the intersection of "SPEAKS CHINESE" and "SPEAKS SPANISH" circles that is not in the "SPEAKS RUSSIAN" circle. So it is \(7\).

Step4: Find Chinese speakers

The number of people who speak Chinese is the sum of all values in the "SPEAKS CHINESE" circle. That is \(6 + 18+7 + 8=39\).

Step5: Find Chinese or Russian (no Spanish) speakers

The number of people who speak Chinese or Russian (no Spanish) is the sum of values in "SPEAKS CHINESE" and "SPEAKS RUSSIAN" circles that are not in "SPEAKS SPANISH" circle. So it is \(6+18 + 30+8=62\).

Step6: Find Spanish speakers

The number of people who speak Spanish is the sum of all values in the "SPEAKS SPANISH" circle. That is \(9+29 + 7+8=53\).

Answer:

a) \(30\)
b) \(8\)
c) \(7\)
d) \(39\)
e) \(62\)
f) \(53\)