In a tourism office, there are 40 employees, including 18 speak English, 22 speak French, 17 speak Spanish, 9 speak English and French, 6 speak English and Spanish, 5 speak French and Spanish and 2 speak all three languages. If information is requested from an employee chosen at random, what is the probability of this employee: a) speaks English or Spanish? b) only speaks Spanish? c) only speaks English? d) speaks French or Spanish? e) speaks one of the three languages?

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Chapter1: Combinatorial Analysis
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In a tourism office, there are 40 employees, including 18
speak English, 22 speak French, 17 speak Spanish, 9
speak English and French, 6 speak English and Spanish, 5
speak French and Spanish and 2 speak all three languages. If
information is requested from an employee chosen at random,
what is the probability of this employee:
a) speaks English or Spanish?
b) only speaks Spanish?
c) only speaks English?
d) speaks French or Spanish?
e) speaks one of the three languages?

Expert Solution
Step 1: Write down the given information

Total= 40 

English = 18 

French = 22

Spanish = 17 

English+French = 9 

English+Spanish = 6 

French+Spanish = 5 

All three = 2 

Probability = favorable / Total 

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