In a group of 25 students, 13 can speak English, 12 can speak Hindi and 6 speak neither. How many can speak (i) Both English and Hindi ? (ii) Only Hindi ? (iii) Exactly one of the two languages ?
We have,
`P(AnnB)=1/8and P(barAnnbarB)=3/8`
`thereforeP(A)P(B)=1/8and P(barA)P(barB)=3/8`
`" "[therefore"A and B are independent"]`
Now, `P(barAnnbarB)=3/8`
`implies1-P(AnnB)=3/8`
`or 1-(P(A)+P(B)-P(AnnB))=3/8`
`or1-(P(A)+P(B))+1/8=3/8`
`orP(A)+P(B)=3/4`
The equation whose roots are P(A) and P(B) is `x^(2)-x{P(A)+P(B)}+P(A)P(B)=0`
`or...