Out of `100` students two sections of `40` and `60` are formed If you and your friend are among `100` students what is the probability `(i)` you both enter the same section `(ii)` you both enter the different sections.

Answer

N/a

Explanation

Let `A=` section of 40 students
`B=` section of 60 students
No. of ways of dividing 100 students into two sections of 40 and 60 students `=.^(100)C_(40)`
(a) No. of ways that both enter the section A
`=.^(2)C_(2)xx.^(98)C_(58)=.^(98)C_(58)`
No.of ways that both enter the same section
`=.^(98)C_(38)+.^(98)C_(58)`
Probability that both enter the same section
`=(.^(98)C_(38)+.^(98)C_(58))/(.^(100)C_(40))`
`=(|__40|__60)/(|__100)[(|__98)/(|__38|__60)+(|__98)/(|__40|__58)]`
`=(|__98)/(|__100)[(|__40)/(|__38)+(|__60)/(|__58)]`
`=(40xx39+60xx59)/(100xx99)=5100/9900=17/33`
(b) Probability that both enter the different section
`=1-` probability that both enter the same section
`=1-17/33=16/33`