Question

In a class, 90% students are Pashto-speakers. Among the Pashto speakers, 80% have learnt
English. What is probability that a student is Pashto-speaker and has not learnt English?

Answer 1

Let

PASHTO be the event that the  student is a Pashto speaker

ENG be the event that the students learnt English

Given ,P( PASHTO) =0.90

P( ENG I PASHTO) = 0.80

To find P( PASHTO ENG^c)

where ENG^c is the event that the student did not learn English

We know that ,

P( PASHTO) =P( PASHTO ENG^c) + P( PASHTO ENG)

P( PASHTO ENG^c) = P( PASHTO) -P( PASHTO ENG)

Now ,

P( PASHTO ENG) =P( ENG I PASHTO) *  P( PASHTO) = 0.80*0.90=0.72

Therefore ,

P( PASHTO ENG^c) = 0.90 -0.72 = 0.18

Probability that a student is a Pashto speaker and has not learnt English = 0.18