Question

Among a group of 100 people, 68 can speak English, 45 can speak French, 42 can speak Spanish. 27 can speak both English and French, 25 can speak both English and Spanish, 16 can speak both French and Spanish, and 9 can speak all three languages. Pick a person at random from this group, what is the probability that this person can speak at least 1 of these languages?

Answer 1

Explanation:

Given

No of People who can speak English is
`n(E)=68`

No of People who can speak French is
`n(F)=45`

No of People who can speak Spanish is
`n(S)=42`

No of People who can speak both English and French
`n\left ( E\cap F\right )=27`

No of People who can speak both English and Spanish
`n\left ( E\cap S\right )=25`

No of People who can speak both French and Spanish
`n\left ( F\cap S\right )=16`

No of people who can speak all languages is
`n\left ( E\cap F\cap S\right )=9`

no of People who can Speak at least one Language is

`n\left ( E\cup F\cup S\right )=n\left ( E\right )+n\left ( F\right )+n\left ( S\right )-n\left ( E\cap F\right )-n\left ( E\cap S\right )-n\left ( F\cap S\right )+n\left ( E\cap F\cap S\right )`

`n\left ( E\cup F\cup S\right )=68+45+42-27-25-16+9=96`

Probability that Randomly selected can speak at least 1 of these languages

`P=(96)/(100)=0.96`